An election district is "anchored" in a jurisdiction in the purest sense if the district is wholly contained within the jurisdiction. For example, the Texas Constitution requires that state house of representative districts be located wholly within a county (with a few specific exceptions). All of these house districts are thus anchored in the county, but the question then becomes whether districts wholly within a county are anchored in a particular city or neighborhood.
An election district may be called "anchored" in a jurisdiction (such as a county, city or neighborhood) even if it contains more than one jurisdiction if the voters of one jurisdiction constitute at least a majority of the total of voters in the district. The bigger the majority, the more secure the anchor. Variables in the definition include:
The key concept is that the voters of an anchor jurisdiction have the potential ability to elect the person of their choice without much, if any, regard to the vote of any other jurisdictions in the election district. Of course, the ultimate outcome of elections is more complicated. It is possible that even when a jurisdiction has a majority, or nearly so, of a district, the elected candidate may come from outside the jurisdiction especially if the voters in a smaller jurisdiction vote overwhelmingly for one candidate and the voters in the larger or anchor jurisdiction split more evenly. The 2012 election of Lloyd Doggett is an example because the voters of Travis County are not even a majority of the voters in congressional district 35.
I hope this helps.