By putting different combinations of exons together, our cells can make different mRNAs from the same gene. This process, known as "alternative splicing," allows our cells to use the information in our genes in different ways. For example, for many proteins, one version (or "isoform") is stuck into the cell membrane, while another, shorter, version is free-floating. Thanks to alternative splicing, our cells can make many more proteins than we have genes.
More-complex organisms like humans don't typically have more genes than simpler organisms. Rather, our genomes have more sophisticated control mechanisms that allow our genes to be used in more ways, leading to greater complexity.