One of the key post-campaign activities for Destiny 2 players to check out after finishing the new Curse of Osiris DLC expansion's campaign are Lost Prophecies. Completing these reward you with unique new, Vex-style weapons, but you don't immediately gain access to any of this. Here's how to unlock Lost Prophecies.
After finishing the campaign, speak with Brother Vance at the Lighthouse on Mercury. He'll provide you with a mission to complete some Adventures. Once you've done three of them, you'll unlock access to Heroic Adventures. These are more difficult versions of standard Adventures with a recommended Power level of 300 and Nightfall-style Modifiers to contend with. While difficult, you can thankfully respawn. Completing one of these will earn you a variety of rewards (including a new shader and emblem), and you'll be able to speak with Vance to move things along.
At this point, he'll provide you with your first Lost Prophecy quest. You'll receive an item that needs to have certain requirements fulfilled; for instance, you might have to farm Heroic Public Events or chests to obtain a specific type of item that must be consumed. (This can take the form of a single blue item, or a green version–in which case you'll need to acquire 10 and then trade them into Vance.) Once you're done that, head back to the Lighthouse, speak with Vance, and activate the Forge. From here, you can craft the first of the new Vex weapons–check out one we got above. It's unclear at this point exactly how often you can repeat all of this, but there are a number of weapons and Lost Prophecy "verses" to complete.
Even aside from these, there are numerous new weapons in Curse of Osiris to obtain. There's also a variety of new gear, new Exotics, and tons of new Eververse cosmetics to obtain through the newly refreshed Bright engrams. As noted above, the expansion also introduces a new (if somewhat brief) campaign set on Mercury, additional Crucible content, and more.