I have heard that fresh water exists on the surface of the desert because of a difference in elevation of the desert, causing the underground water to pop up. Is it the reason why oases exists?

Natural oases form when springs, created when underground aquifers allow fresh water to pool or flow on the ground surface of deserts, creating a fertile region.

A human made oasis occurs when humans create fertile region in a dry or arid region, such as a desert. The supply of water in human made oases is from underground water supplied by human made wells or water bores. Because wind-blown desert sands can damage or destroy wells, sturdy trees (such as palm trees) are planted around the periphery of the oases.