This is a great set-extending strategy that'll give you a bigger pump and faster muscle growth. You'll usually see people doing this with squats, but try it with the chest press, shoulder press, triceps extension, and row variations.
The basic principle of the one-and-a-quarter rep is that it places more work in the disadvantageous or weak part of the lift. For example, in the squat and chest press, it's at the bottom of the lift.
Consider the triceps extension (shown in video). The triceps are stretch-shortening muscles. This means increased muscle fiber recruitment when the contraction is preceded by a stretch. Using this stretch-shortening reflex to your advantage guarantees better motor unit activation.