There are other ways how to make crossover, for example we can choose more crossover points. Crossover can be rather complicated and very depends on encoding of the encoding of chromosome. Specific crossover made for a specific problem can improve performance of the genetic algorithm. After a crossover is performed, mutation take place. This is to prevent falling all solutions in population into a local optimum of solved problem.
Mutation changes randomly the new offspring.
For binary encoding we can switch a few randomly chosen bits from 1 to 0 or from 0 to 1. The mutation depends on the encoding as well as the crossover. For example when we are encoding permutations, mutation could be exchanging two genes.