Leasing rights means when a music artist buys your beat they do not own the beat exclusively. The beat is usually lower in price because it will be sold multiple times to multiple music artists.
Exclusive rights means the beat will only be sold once to a single music artist. That artist then owns the beat.
Free Downloads are NO FREE BEATS. Only non-commercial / non-profitable use. The purpose of free downloads is to offer the possibility to record / write a song to them and have a test-drive to see if the final results are worth it investing in a license. The free downloads contain tags and these tags may not be removed under any circumstances.