Authorising the app means that the following information will collected and used in the creation of leagues and competitions that rely on Strava data:
Strava Club member list. Names, athelete_id, avatar, lcoation. No age though.
Segment information. Segment name, elevation, distance etc.
Segment efforts. Athete_id, time, power, whether KOM or PR etc.
Click here to find all your currently authorised apps
it is also here that you can revoke authorisation.