In Diablo 4, you'll earn renown as you work on completing each major zone on the map. In the Diablo 4 beta, you'll earn renown in the Fractured Peaks by unlocking waypoints, Altars of Lilith, and clearing side dungeons, among other things.
Renown is basically a rewards track for character specific bonuses and account-wide ones as you complete objectives in the area. Here are the renown reward tiers available in Diablo 4 beta so far:
(Image credit: Blizzard)