What do we mean when we say a horse broke early?

When a horse changes from one gait to another we call it "breaking" gait.

A horse that breaks early is changing gait, up and down, before the rider or driver asks. A lazy horse may drop out of canter or trot, whilst a more active and lively one may anticipate an upward transition. (It can also mean that the rider inadvertently asked the horse to stop or misjudged a balance request).