It’s currently not possible to mark a conversation as resolved or pick a solution.
Discourse should be shipped with the Discourse Solved plugin which allows the OP to accept a reply as a solution, in which case it only has to be activated. The steps are pretty simple and explained in the following blog post:
The plugin was already enabled but didn’t have the option “Allow users to select solutions on all topics” enabled. Can you know see this Accept button?
I'm not sure, if you receive a notification, when a reply of yours is chosen as the solution, thus the reply.
Yep, I can see it...
...and have used it already. 
Thank you!