In cycling and other race sports:
In various types of race run under handicap systems which involve some participants receiving an advantage in terms of time or distance, the scratch mark is the datum from which the handicaps are calculated - the full distance of the race or the time at which the last competitor starts. By extension the competitor who receives zero advantage from the handicap system - thus, presumably, the strongest competitor - can be referred to as being "on scratch" or as "the scratch man" (or woman, obviously).
By extension, a scratch race is a race run without handicapping, i.e. with all competitors starting together or with no particular advantage - a normal race, in other words. In track cycling, the distinction is most commonly used in Australia, where there is a strong tradition of handicapped racing. Middle-distance scratch races have been a mainstay of the sport at mass participation levels in many other places (in the UK most track league meetings end up with a 20 km race for all competitors). A scratch race (now 20 km, previously 10 miles) has also long been an event at the Commonwealth Games, and as of the 2002 season 10 km women's and 15 km men's scratch races are to be held at the World Track Championships.