all-around

1. Comprehensive in extent or depth: a good all-around education.
2. Able to do many things well; versatile: an all-around athlete. See synonyms at versatile.

adjective

1. Covering a wide scope: all-inclusive, all-round, broad, broad-spectrum, comprehensive, expansive, extended, extensive, far-ranging, far-reaching, general, global, inclusive, large, overall, sweeping, wide-ranging, wide-reaching, widespread. See specific/general.
2. Having many aspects, uses, or abilities: all-round, many-sided, multifaceted, protean, various, versatile. See ability/inability, same/different/compare.

The adjective has one meaning:

Meaning #1: many-sided
  Synonyms: all-round, well-rounded