Your rank is where you place in a series of numbers. For example, your specifically assigned division may have 300 members. Your rank of 61 means you are 61 positions from first place with 239 players behind you. Each week, the rankings are compiled and you are, depending upon your rank in the series, either promoted, retained in place, or demoted to the next lower division. Traditionally this slotting is accomplished by thirds - top third is promoted, middle third retained in place, bottom third reduced one level. The “value” of your rank is determined by total coin winnings for that week (losses are not included in the calculations).
And yes, you do get a weekly notification of your ranking. It is posted every Monday morning (if you played any coin room matches the previous week).