Just like it's possible to get COVID again and again. Neither your immune system nor COVID variant are stay the same over time.

Several ways.

To start with, I'm pretty sure it was established early on that the various vaccines don't prevent infection necessarily, but rather reduce the severity of the symptoms.

Vaccines are always one step behind, like they are for Influenza. You can get vaccinated against last years, and still catch this years.

Maybe the vaccine that was given was not given or stored correctly. There were also stories of anti-vaxxer medical staff giving fake vaccinations to people.

And biology is weird and complicated. Given the large human population and diversity, at some point there'll be an exception.

Vaccines aren't total protection. Notably, you can get chicken pox as a child despite having been vaccinated for it, it simply reduces the severity.