The reproductive system is essential to life, it is how we create new life. Biologically speaking, reproduction is the meaning of life.
There are two types of reproduction; asexual (essentially cloning oneself) and sexual (mating with another). Sexual reproduction increases diversity and is the key to evolution. 99% of all organisms can reproduce sexually.
Though reproductive organs can be diverse, they exist for the same reason. Females produce eggs, this takes lots of time and energy and results in the production of very few egg cells. Males, however, produce lots of fast moving sperm that is constantly being replaced. All organisms produce at least one of these (hermaphroditic organisms contain both) gametes which are formed during meiosis.
All reproductive systems are designed around the creation,storage and the delivery of these gametes so a species can go on living.
From Crash Course: Biology on YouTube presented by Hank Green.