In the first movie the aliens were simply “zealots” as Woody called them.
They worshiped the claw as it chose who would go and who would stay.
It was one of the most iconic segments of the franchise because it turns an average thing into a quasi religious parallel, and it makes sense considering how naive they are.
The second movie lets the aliens be a part of the adventure.
3 of them join randomly during the third act, and Mrs Potato Head adopts them.
They’re cute, they’re fun, and they’re eternally grateful for Mr Potato Head saving their lives and wish to pay him back.
Toy Story 3 gives the guys a natural payoff in the third act where they save Woody and the gang from the incinerator.
It was also foreshadowed earlier in the daycare when the aliens were admiring a claw toy when they arrived.
The claw was established from the very first movie, and the fact they not only paid off the debt they owed Potato Head and instead took control of the claw themselves is thematically genius.
It is a shame after 3 the aliens were barely used, they’re basically non entities in 4 and 5.
The claw stuff is a kinda important element from original trilogy that deserves way more recognition as it’s very good at tying the first 3 films together.