First off, removing this activity is safe to do, especially in the latest version of the Crittercism SDK.
Within the context of Crittercism, the Notification activity provided the agent the ability to pop up a message to the user within the app. To go a bit deeper, whenever your application crashes Crittercism provides a list of users affected by that crash within the crash report. Via an interface on the Crittercism portal, you were able to send a notification to the users affected with a message such as "Hey sorry about the trouble, we're working on this now and will let you know when the bug has been fixed" or something along those lines. This message would pop up on next app load.
This feature was deprecated last year in lieu of customer communication via partnerships with companies like UserVoice, Helpshift, etc and I'm sure there will be others.
You can update to the latest Library (found here : Crittercism Android Downloads) and see the changes Crittercism has made for yourself.