Sexual reproduction
The process in which gametes produced by sexual reproductive structures fuse together is called sexual reproduction.
Two organisms contribute, one gamete each. The gametes fuse, and the cell that results carries characteristics from both. That mixing is the point of the whole arrangement — it is why sexual reproduction can produce offspring unlike either parent, and asexual reproduction cannot.
Structures shaped for sexual reproduction are found in the organisms that are evolutionarily more advanced. The structure built specially for it in plants is the flower. In animals it is a pair of reproductive systems, female and male.
Why the offspring differ
Gametes are made by meiosis, which halves the chromosome number and shuffles what goes into each gamete. Two shuffled halves then combine. A new organism therefore starts life with a combination that has never existed before, which is where new characteristics — and eventually new species — come from.