P(A and B) = P(A)P(B), equivalently P(A | B) = P(A).
The traps, both common:
Independence is not the same as mutual exclusivity. Mutually exclusive events with positive probability are strongly dependent - if one happened, the other definitely did not.
Pairwise independence does not imply mutual independence. Three events can be independent in every pair while the third is determined by the other two. Interviewers construct exactly this counterexample.
Zero correlation does not imply independence either, except for jointly normal variables.