The Toy Story 3 ending is Andy handing his toys to Bonnie, taking one last moment to play with them, and driving off to college. In my opinion, it is the cleanest goodbye in the series, because the story lets Andy leave as a person and lets the toys continue as toys.
What actually happens is simple. Andy gives all the toys to Bonnie and says goodbye, the toys accept the change and begin a new life with her, and a closing sequence shows that Barbie, Ken and Big Baby have helped make Sunnyside a better place for the toys there. Lotso, by contrast, ends the film strapped to the front of a garbage truck, so the daycare's tyrant does not get a comfortable ending.
It could be argued that the film is really about being chosen. The toys fear being thrown away at the start, nearly are thrown away at the landfill and incinerator, and finally are chosen on purpose by Andy, which is the opposite of the mix-up that started the story. That being said, the film does not pretend the loss is painless. The toys lose the one child they have known since Toy Story (1995), and the final scene gives them time to feel it.
Is Toy Story 3 the last movie? No. Pixar returned with Toy Story 4 in 2019, which picks up with Woody being played with less than he used to be in Bonnie's room, and Toy Story 5 followed in 2026. If you want the ending to stand alone, you can stop here. The Toy Story timeline shows how the later films follow on.