It means the amount of times a player has watched a reply done by you. For example if you click on a player on the top 50 list in the beatmap selection, it'll bring you to the replay view. There's also ways players can directly save or share replays with others.
Additional Info Edit: Oh, and if all keys besides your shift key work for the binding, then my only guess is it's your keyboard. Sorry I have no other ideas for solutions to that issue, unless there's another game setting that's interfering with the shift key.