To add a quick description of what the numbers mean. For example in "Casual rank: 27. (1822 ± 40, Top 21.8%"
”27." is your rank among active players. Being active means having played around ten matches during the last month or 5 matches today if you were inactive before. These match numbers are different for every player, because activity is defined by the uncertainty ("± 40") being below a global cutoff.
"1822" is your rating as estimated from your most recent game. It is recalculated daily in order to make fine adjustments based on the opponents you played against. For example when you played against a smurf and lost rating, this rating will be restored if the system successfully identifies the smurf. Your visible rating will also start "decaying" as soon as your uncertainty rises above 20. Decay is proportional to uncertainty.
"± 40" is your rating uncertainty. It will generally decrease the more games you play. The only exception is if you start playing completely outside of your expected skill range. Uncertainty slowly increases over time, linear to the square root of days since your last game. Besides being used for decay and as the activity threshold, uncertainty specifies how much your rating will be affected by upcoming games. Very active players with a low uncertainty will only see rating changes in the single digit range, while the rating can jump hundreds of points for a newbie or an old player coming back.
"Top 21.8%" this is your percentile among all active players. The lower, the better.