Asexual Reproduction is the process of reproduction in which the offspring  arise by a single parent and there is no fusion of gametes.The offspring inherits the characteristics of the parent and is identical to it.

Budding and Multiple fission are some examples of Asexual Reproduction

Budding-in this process the offspring arises from the outgrowth in the parent cell.The outgrowth or the bud gets a separate nucleus and then detaches from the parent cell forms an independent organism

Multiple Fission-In this process the nucleus of the parent cell divides numerous times to form numerous nucleus and forms several daughter cells.

Hope this helps :)
Asexual method of reproduction is where an offspring takes birth from a single organism. The offspring looks exactly as the parent.
Budding and Fission are examples of asexual mode of reproduction.