People chant Hare Krishna for lots of reasons. Some people are just curious. Some want material benefits, or relief from anxiety. But the best reason to chant Hare Krishna is to get to know Krishna, the Supreme Personality of Godhead.
Just as you can get acquainted with someone by associating with him, you can find out about Krishna by associating with His name because the sound “Krishna” is the same as Krishna Himself. It’s called the sound incarnation of God. “Hare Krishna” is a call to the Lord to engage us in His service. The process is simple and sublime.