For better: Beyond the obvious "your rating in whatever format you play chess in gets better" answer, a few others:
- You're scalping higher-rated players in slow/serious games.
- Consistently beating lower-rated players (allowing no comebacks from won games)
- Seeing single and double-motif tactical shots within seconds on the board.
- You're realizing this game just keeps getting tougher :)
If you were to look at a game you played a month/year ago and "cannot" believe you used to play that way ... I guess that's a sign as well!

How do you know whether you are getting better at Chess or getting worse?