What do "Your best BKR" and "Your best rating positions" tables show?

These tables which are displayed on the main page show your current BKRs and positions (see Ratings link in the menu column) sorted by its values (the best is the first). The values written by the italic font mean the provisional BKR and positions, otherwise (normal font) the established values are used. If both (provisional and established) positions appear at one row, for example "9. (13.)", it means that your position (when only established BKRs are counted) is 9 and you are at the 13th position in all-BKRs table for this game type.
You can specify the number of rows of this table displayed on the Main page at your Settings page (Number of my best BKR shown on the main page).