Each type of animal companion is a little different.

Bear (also Giant Badger, Wolverine)

Acts: After ranger

Advantage: The bear gains temporary hit points equal to its level each time it hits with an attack.

Champion Feat

The temporary hit points increase to double its level.

Boar (also Spiky Lizard)

Acts: Before ranger

Advantage: The boar gains a +1 attack bonus when it moves before its attack during the same turn.

Eagle (also Falcon, Hawk, Owl, Vulture)

Acts: Before ranger

Advantage: It flies! Its melee damage die is dropped by one size (d6 at level 0).

Panther (also Lion, Tiger)

Acts: Before ranger

Advantage: The panther's crit range expands by 2 against enemies with lower initiative.

Snake (also Giant Spider, Poison Toad)

Acts: After ranger

Advantage: The snake also deals ongoing poison damage equal to twice your level on a natural attack roll of 18+.

Champion Feat

The ongoing damage is three times your level instead.

Epic Feat

The ongoing damage is four times your level instead.

Wolf (also Big Dog, Coyote, Hyena, Jackal)

Acts: After ranger

Advantage: The wolf gains a +1 attack bonus against enemies its master attacked the same turn, or against enemies engaged with its master.