Do bananas have seeds? The answer to this question can be summarized as such:

If we are to define the word "fruit", we could say it's a mature ovary containing seeds. In fact, bananas are more precisely referred to as a berry! Wild banana varieties carry big seeds that would make it difficult for us to eat them (in turn, this would make it difficult for banana growers to sell them!).
The banana we all eat is cultivated with the precise purpose of being made seedless (or with seeds so small they're barely visible): this is achieved by cultivating triploid varieties (which means they have three sets of genes, instead of the two sets that are normally found in wild varieties). Because of this, sexual reproduction of these modified bananas is impossible, and they have to be grown from offshoots of the parent plant.