The Hot/Crazy Scale is a graph used to display someone's hot-to-crazy ratio. As Barney explains in How I Met Everyone Else, a person is allowed to be crazy, as long as they are equally hot. Ideally, you want your date to be above the diagonal line, indicating that they are hotter than they are crazy. There does appear to be some bias however, as shown by Barney's diagram, which indicates that someone who is the maximum level of crazy does not have to be the maximum level of hot in order to be equal to/above the diagonal line.
The diagonal line is known as the Vicky Mendoza Diagonal by Barney, after a girl he dated who jumped back and forth across the line by shaving her head, then losing ten pounds, then stabbing Barney with a fork and finally getting a boob job.
The bottom-right corner of the scale is dubbed the Shelly Gallebsy zone by Barney, after another girl he dated who fell into that area after gaining twenty pounds and trying to kill him with a brick. Barney explains the Hot-Crazy scale to the gang after Ted introduces them to Blah Blah, his crazy girlfriend at the time.