what's the meaning of "around"

Solution 1:

This seems to be a variation of preposition definition 1.1 in ODO:

(Of something abstract) having (the thing mentioned) as a focal point: our entire culture is built around those loyalties

This definition seems to be a metaphoric generalization of the more concrete senses related to surroundings of places.

Solution 2:

Around was not the best choice for the sample sentence. The more accurate replacement would be as follows:

...become the best it can possibly be in those things which it already does so well.

The general expression is "to be the best in something," not "around something," or even "together with something."