Since ages, we’ve been striving to reduce the gap between ourselves and God. There are two ways to do this: one way is to elevate humankind towards Divinity — this is called Siddha, and the person who achieves this state is believed to have attained perfection.
The second way is to bring God to human level in avatar form. Here, Divinity manifests itself for the sake of humankind. So, man rising up to God is Siddha; God coming down, because he cares for you, and wants to communicate directly with you, is avatar.