Bg 1.15

pāñcajanya hṛṣīkeśo
devadatta dhanañ-jaya
pauṇḍra dadhmau mahā-śakha
bhīma-karmā vkodara

Word for word: 

pāñcajanyam — the conchshell named Pāñcajanya; hṛṣīka-īśa — Hṛṣīkeśa (Kṛṣṇa, the Lord who directs the senses of the devotees); devadattam — the conchshell named Devadatta; dhanam-jaya — Dhanañjaya (Arjuna, the winner of wealth); pauṇḍram — the conch named Pauṇḍra; dadhmau — blew; mahā-śakham — the terric conchshell; bhīma-karmā — one who performs herculean tasks; vka-udara — the voracious eater (Bhīma).

Translation: 

Lord Kṛṣṇa blew His conchshell, called Pāñcajanya; Arjuna blew his, the Devadatta; and Bhīma, the voracious eater and performer of herculean tasks, blew his terric conchshell, called Pauṇḍra.

both of them has blown there conchshell pāñcajanya hṛṣīkeśo, Lord hṛṣīkeśa has blown pāñcajanya.

devadatta dhanañ-jaya, dhanañ-jaya blew up his conchshell named devadatta.

pauṇḍra dadhmau mahā-śakha, the giant Shankha mahā-śakha Bhima himself was giant, his strength was like that of a giant and his paraphernalia was also giant, his conchshell was also giant names Paundra.
bhīma-karmā vkodara, so Bhima the name itself was like Hercules. Extremely strong so in English there is a word called Herculean, so Hercules was a character in Greek or Roman tradition he was a giant strength and he could do huge amount of work so many of the character in Greek or Roman characters they are derivatives from the Vedic tradition. If we look at the thought of Socrates  Philosopher Socrates friend’s wife passes away and his brother are lamenting there Socrates consolidated him by giving 5 reasons about mortality of the soul and those reasons are practically identical to the second chapter of BG where Sri Krishna is telling Arjuna about the immortality of the soul. After Kurukshetra war from the Indian mainland there were many expatriates which went away to various parts in the world. And over the centuries when power from Hastinapur became weaker and weaker the connection with the parent culture became mutinous and some local culture derivatives also came up that is why there are similarities between Vedic culture and other cultures of the world and there are differences also. Vedic patriarchs consider Greek or Roman culture as expatriates Vedic civilization, Srila Prabhupada talks about this and it is mentioned in Lilamrita also. dara means stomach and Vrika means giant so vkodara refers to as Srila Prabhupada mentioned is voracious eater. Bhima was extremely powerful and power doesn’t come out of thin air a person who does lot of powerful work gets power by eating

bhīma-karmā, his name is Bhima and his Karma is also Bhima, here he is referred by another name vkodara. A lot of the food was given to Bhima as Bhima was bhīma-karmā vkodara he eat more and his does tremendous work e.g. he kept all Pandavas and mother Kunti on his shoulder and kept running during fire in Lakshagraha.

Depending on different bodies amount of work etc different people eat different amount of food and if we are eating less we shouldn’t think that I am more sense controller than others it is consistency which is required not that today food was very good so I eat so much and other day less food as it was not so good. It is natural to take little more. On a regular basis if someone needs more food that is not lack of sense control, in Vaishanav culture we also have Raghunath Das Goswami who take little butter milk once in three days on the other hand we have Bhima, fasting was very difficult for Bhima. We got Pandava Nirjala Ekadasi because of giant apatite of Bhima.

Bhima told his grandfather Vyasa Deva who was like his grandfather, this was a system in Vedic system that for dynasty to go on if a women in the dynasty doesn’t have a husband then the brother-in-law can impregnate her and in such cases the offsprings who are born are not considered to be son’s of that brother-in-law they are considered to be her son’s and the son’s of the deceased husband so if the brother-in-law is just begetting so that the dynasty can go on then the brother-in-law is not considered to be father that is why in Mahabharat although it was Vyasa-deva through whom Dhritarashtra and Pandu are born they don’t refer Vyasa deva as father nor do Pandav’s refer to them as grandfather because that is contingent arrangement because of emergency that particular arrangement is done. In modern time this can be considered controversial and scandalous also, the point is in today’s society focus is too much on lust and sex although this was always part, important part, significant part of human culture but now a days is predominant part and because of this in all relationships many people is not able to think beyond the carnality of this relationship. In earlier culture, dynasty was very important and to continue the dynasty was very important. So the focus on this thing is not on the immorality or the sensuality, there was just one time contact between Vyasa Deva and Ambika and Ambalika and after that there is no other contact at all and also no body considered that they are contaminated, Vyasa Deva was still respected as great sage and compiler of Vedic literature and Ambika and Ambalika were not considered as unchaste in anyway the point in this is continuation if the dynasty so although from seminal point of view Vyasa Deva was considered their grandfather but he was never referred that way he was referred primarily as great sage and everyone respect him accordingly. (But this practice is forbidden in Kalyuga like many others e.g. animal sacrifice.)

So Bhima tell his problem of fasting to Vyasa Deva and he informed Bhima about glories of Ekadasi and he told Bhima that you must fast on Ekadasi which was not possible for Bhima so Vyasa Deva has arranged one special Ekadasi Nirjala for him, Vyasa Deva has that potency and he told if Bhima will fast on this Ekadasi he will get benefit of fasting for all Ekadasi in a year.

Srila Prabhupada has elaborated on the name hṛṣīkesa and dhanañ-jaya here.

hṛṣīkesa, Krishna is the controller of the senses what is the meaning that there are two meaning one is objectively He is always the controller and other is subjectively we accept Him as controller and then we voluntarily agreed to be controlled by Him. So objectively means right now I am speaking and I think I have right and power to speak   but suppose I develop a bad throat in that case I am here and my throat is here but I will lose the power to speak, so objectively it is a reality that my senses are not under my control although I call my senses as mine and although frequently I am able to control them at the same time there are times when I will not be able to control them, sometime people get paralysis or Parkinson or diseases like that and they cannot control their own limbs. So the point here is we have limited powers and even those power can be taken away at any time. So Krishna is, objectively speaking, the controller and based on our past Karma He gives certain level of control to our body and our senses so now our perfection is recognize the objective reality and then subjectively accept Krishna as the controller. That means Krishna you are my master and my senses are your and I meant to be your servant so please engage me in your service, please accept me as your servant. So when we understand this and accept this principal then we are moving towards spiritual reality that is how the definition of Bhakti is Hrishikesha Hrishikena Sevati Bhakti Uchayate, Hrishikena with senses we serve the Lord of senses.

Pāñcajanya, there is a story in SB how there was a demon pāñcajanya whom Krishna killed. He had a conch and Krishna took that conch. This is just the historical narrative when Krishna appeared how He got the conch but actually conch is His eternal associate and paraphernalia and in spiritual world it is always there with Him but when He appeared in this world there is a particular historical narrative by which his associated comes and meets Him and His paraphernalia becomes His.

dhanañ-jaya, now Arjuna is called Dhananjaya means one who gets Dhana when required Dhana, this is because he accumulated wealth (He went in north and searched for wealth and he got lot of wealth there) when Yudhisthira Maharaj need it for doing Rajasuya Yajna. Also he got the wealth of spiritual knowledge which is the ultimate wealth.