Sexual Reproduction:
This occurs when both male and female gametes (egg and sperm) fuze to create a zygote.
This process is required in order to adapt to new environments through genetic diversity, as those with more favourable characteristics survive and pass them on in their offspring. For example, a genetic disease would have less chance to be passed on through sexual reproduction over asexual reproduction, this is because asexual offspring are 'clones' of the parent. However, for sexual reproduction to occur, there must also be a partner or mate present.
Asexual Reproduction:
This is the process of creating identical copies or "clones" of an organism though Mitosis, Meiosis or Binary fission. Unlike sexual reproduction, asexual organisms don't require a mate. Thus one individual can replicate itself over and over. The process is shorter, which allows for more offspring faster. Artificial asexual reproduction is very beneficial in order to replicate organisms with favoured traits, such as the cuttings of a particular fruit tree that produces better/more fruit than others of its species.
http://www.pulsarmedia.eu/r_life_in_ocean_%26_sea_wallpapers_1_starfish_40902.html
http://www.nickgarbutt.com/photo-galleries/borneo-and-se-asia/frogs