The system consists of five classes indicating the technical difficulty of the hardest section. Class 1 is the easiest and consists of walking on even terrain. Class 5 is climbing on vertical or near vertical rock, and requires skill and a rope to proceed safely. Un-roped falls would result in severe injury or death. Originally, Class 6 was used to grade aid climbing. However, the separate A (aid) rating system became popular instead.
The original intention was that the classes would be subdivided decimally, so that a route graded 4.5 would be a scramble halfway between 4 and 5, and 5.9 would be the hardest rock climb. Increased standards and improved equipment meant that climbs graded 5.9 in the 1960s are now only of moderate difficulty. Rather than regrade all climbs each time standards improve, additional grades were added at the top – originally only 5.10, but it soon became apparent that an open-ended system was needed, and further grades of 5.11, 5.12, etc. were added.
While the top grade was 5.10, a large range of climbs in this grade were completed, and climbers realized a subdivision of the upper grades were required. Letter grades were added for climbs at 5.10 and above, by adding a letter "a" (easiest), "b", "c" or "d" (hardest).
The system originally considered only the technical difficulty of the hardest move on a route. For example a route of mainly 5.7 moves but with one 5.11b move would be graded 5.11b and a climb that consisted of 5.11b moves all along its route, would also be 5.11b. Modern application of climbing grades, especially on climbs at the upper end of the scale (>5.10) also consider how sustained or strenuous a climb is, in addition to the difficulty of the single hardest move.
That's the sixth job in two weeks.
