Companion Characters are NPCs that directly will assist you in battle with a myriad of different abilities.
Instead of bogging up combat with a bunch of NPCs to track, the companion system helps to give the feel that the NPCs are assisting you while still never taking center stage in any conflict. This story is about you and your fellow PCs, not the NPCs (though they are extremely important).
If a NPC has the Companion tag, it will have its ability or bonus written out under the description bar in their character information tab (check the characters tab to find it). You gain the passive ability granted from your companion and can use any power they provide through your own actions. (usability depends on the power used). Unless otherwise noted, companion powers gain no bonuses from anything your character has (like feats and the like). Additionally, the powers are effectively shared with your whole group, so if a companions power is once per encounter, it can only be used once that encounter regardless of who used it.
You can only use one companion per extended rest (i.e. you can pick which one you want to assist you after the rest) or whenever you return to the Yggdrasil where your companions will be waiting.
Companions are powerful tools, don’t forget to allow the NPCs to help you on your journey through the wastes.