Your reputation on Steemit is increased by other users upvoting your posts. Similarly downvotes decrease your reputation.
For each of your posts the reward shares of the votes made (i.e. your share of the reward pool) is added to your reputation so that it increases. Similarly the rshares from flags (downvotes) are deducted from your reputation.
However there are some small complexities:
- Users with negative reputation cannot impact other users' reputation.
- A downvote will not impact your reputation unless the downvoter has a higher reputation than you.
The underlying reputation figure is actually a large number (since reward share numbers are large) and is converted to the reputation level using (broadly):
log10(underlying reputation figure) + 25.
Reputation level for a new user is thus 25. It is more difficult to move from one reputation level to the next as your reputation increases due to the log10 function.
Good articles are here:
https://www.steem.center/index.php?title=Reputation_System
https://steemit.com/steemit/@arcange/what-is-steemit-reputation-and-how-does-it-works