Every horse owner should know how to check a horse's vital signs. This can alert you to trouble, give you some indication of how serious it is, and give you important information to relay to your vet if you need to call them.
Here's a great guide to checking your horse's vital signs, and a pretty nice wall chart to go with it.
The only thing I would add is you also need to know your own horse. Every horse is an individual, and normal vital signs may vary slightly. It's also important to know your horse's normal demeanor and behavior, as even small changes in behavior, stance or appearance can signal trouble brewing. This includes things like normal behavior around other horses, in the stall, at feeding time, and when grooming and riding; how the horse holds its body and positions its legs; and the horse's expressions and attitude - the face, ears, eyes and lips can tell you a lot. Horses can be stoics - this makes sense since a horse showing pain or illness would be attractive to predators - but they vary on this spectrum as well.