As Ac9 said it is usually worn after somone related to the club/s has passed on. Some clubs have yearly commemoration days to pay tribute to the dead over that year. Man City had that last weekend I think, with a minutes silence and the wearing of the black arm bands.
The 50th Anniversary of the Munich Air Disaster is on the 6th of February and there will be special tributes including a one off Busby Babes style kit in the local Derby against City, which takes place on the 10th of Feb.
England will also pay tribute when they play on the day of the anniversary.
They will play against Switzerland on the 6th of February at Wembley.