Helltides are a Diablo 4 feature where part of a region becomes corrupted (turns red on the map). You need to be playing in World Tier 3 or higher difficulty for this to happen. The monsters in an area affected by a Helltide have a higher level than the player, making them more difficult to defeat. However, they also drop more loot and Aberrant Cinders, which is a special temporary currency that can be used to open temporary Helltide Chests in the respective region.
Helltides last for about an hour and occur randomly in the open world. You can tell if a region is under a Helltide by looking at the map or the sky. A Helltide icon will appear on the map, as well as parts of the map being covered in red color, and the sky will have a reddish hue. Once a Helltide is over, all Chests disappear and all Aberrant Cinders will be removed, so no progress is carried over, other than the items you can loot during the Helltide itself.