A tucked up horse is one who's flanks have collapsed inward. This results in an appearance somewhat like a greyhound (except it's normal for the greyhound). It's more obvious in Thoroughbreds, which tend to have a bit of a narrow stomach at the best of times.
Being tucked up can be a reaction to pain, especially in the digestive system. It can also be caused by malnutrition, especially insufficient fibre. A tucked up appearance after work is often a sign of dehydration - meaning the horse needs fluids and possibly electrolytes quickly.
This racehorse being cooled down is showing a bit of a tucked up appearance - it was an extremely hot day and us humans in the stands needed extra water, let alone the horses!