Rivals are your contenders or competitors. In The Sims Mobile, your rivals don't have the same objective nor superiority in a certain activity with you. That is simply the first step to a meaner relationship. Once you've reached Level 2 relationship with other Sims, you can do mean interactions with them and begin the "Declare Rivalry" social event.
Generous These Sims give a bit better daily Login Rewards
Lucky These Sims occasionally give you bonus XP while at home
Mean These Sims get a bonus every now and then when being insulting with others
Competitive These Sims are a bit better at Rival Events
Good Upbringing These Sims are way better at all Events