Pet Focus is a focus effect found on certain items. Pet focus only works for the pets of the following classes Magician, Beastlord, Necromancer. The pet focus does not provide the usual focus effect message like other spell effects; the focus effect is only factored the precise moment when you summon a pet from a spell. Once a pet is summoned, having a pet focus equiped or not makes no difference. Your only reliable means to determine if your pet is focused or not is to send it into combat and compare the before/after performance.
Pet focus is a complicated effect that varies between pets, focus and classes. The benefits of a pet focus for a magician will not be identical for a necromancer or beastlord, and vice versa. This is due to the focused pets actually being a completely unique dev-built pet based on the summoning spell and the focus effect used. It does not acually focus an existing pet - it summons a uniquely built pet designed with that focus effect bonus in place.
Each pet focus works for a specific range of pet spells, and provides no benefit for pets summoned prior to or after the supported range, which can be found in the spell description at lucy.allakhazam.com. The supported levels refer to the level of the summon pet spell - not the actual level of the pet or the level of the player. A pet focus reference can be found at necrotalk.com or at eqmagicians.com.
There are multiple levels of pet focus that provide varying levels of benefit. This includes increasing the pet base hit points capacity, higher maximum and minimum hits - and sometimes even increasing the base level of the pet. Very high-end focus effects also include extra stat bonus such as +avoidance, +shielding, +spell shield, etc.