What that number next to your name actually represents.
A chess rating is a number meant to predict results, not just reward wins. Beat a much higher-rated player and you gain a lot of points, because that result was unexpected. Beat a much lower-rated player and you gain very little, because it was expected. Lose to a lower-rated player and you lose a lot of points, for the same reason. Over enough games, the number settles toward a value that accurately reflects a player's real strength relative to everyone else in the pool.
Most over-the-board and many online ratings are based on the Elo system, created by physicist Arpad Elo and adopted by FIDE (chess's international governing body) in the 1970s. Each player has a single rating number, and after a game, both ratings shift based on the result and the difference between the two ratings going in. A 200-point gap represents roughly a 3-to-1 favorite in Elo's model — not a guarantee, but a strong statistical edge.
Lichess and several other online platforms use Glicko or Glicko-2 instead, a refinement developed by Mark Glickman. The key addition is a second number — a "rating deviation," essentially a confidence interval around your rating. A brand-new player's rating can swing hard after just a few games because the system isn't confident yet about where they truly belong. An established player who's played thousands of games has a narrow deviation, so their rating moves in smaller steps, since the system already has strong evidence of their real strength.
A 1500 on chess.com, a 1500 on Lichess, and a 1500 FIDE rating are three different numbers measuring three different, mostly-separate player pools — they are not directly interchangeable. Each platform's rating pool has its own average skill level and its own history, so the honest comparison is always within the same platform and time control, not across different sites.
Most platforms track separate ratings for bullet, blitz, rapid, and classical, because skill at fast time controls and skill at slow, deep-calculation games aren't the same thing — a player can be genuinely strong at blitz and considerably weaker at classical, or the reverse, and separate ratings capture that instead of averaging it away.
Puzzle ratings use this same general rating-system logic, but measure something narrower — tactical pattern-solving under no time pressure, with no opening prep or endgame technique involved. See How Puzzle Ratings Work for the full explanation of how that specifically applies to the puzzle trainer.
Put it into practice: train tactics on Puzzles, or review a real game on Analyze.