The Companions are one of the 4 factions available in Skyrim. They are more or less the equivalent of the Warrior's guild in Oblivion and have a good selection of combat trainers.
On your first visit to Whiterun, you will be able to start and complete this quest. The man you need to speak to is Kodlak and is usually found in Jorrvaskr in his quarters downstairs.
The Companions can be found to the north up the stairs from the market in Whiterun. In case you don't find it, use your local map and look for a house named Jorrvaskr.
Complete their initiation quest and this achievement will unlock.