I have never heard an exact definition of Squad AI and exactly what it supposed to do.
Furthermore i don't exactly see the problem it tries to solve.
In short: Squad AI gives the individual entities of a squad a level of AI behaviors.
There are a number of different categories and circumstances that can trigger this AI, such as being in combat.
The way the AI works is that an entity will, for instance, search in a radius around it for cover and run for it once combat is initiated.
It can also impact how squads maneuver around objects and path, such as leap frogging rather than moving in a specific formation.
Arguably squad AI gives squads the ability to fight efficiently (and sometimes not so much) without a level of micro from the player. A player can leave a squad in combat and trust that they'll utilize cover, rather than having to manually direct them to choose a specific piece of cover. (Which typically results in a clumped up squad.) The AI often gets squads to naturally spread out.
I personally think it's a major component of what makes the CoH franchise so unique. I think at face value squad AI is more 'different' than 'better', but I do believe it gives all squad based combat much more flexibility and dynamicism, which I personally find 'better'.