So emptying those two tables will rob threads and attachments of their most recent views.
Emptying the session table will logout everyone who is currently logged in. If the user selected Stay logged in when they logged in then they will be automatically logged in again as if they were never logged out.
I am less sure about the implications of emptying the session_activity table. It's probably safe, but it might affect features that rely on user.last_activity in that some users will be robbed of their most recent last_activity time.