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