Compression tights are an excellent article of clothing to have on hand if you are a runner. Not only are they comfortable, easy to wear, wash, and maintain, and are great for traveling, but they offer extensive health benefits - especially in regards to recovery and keeping your legs fresh and ready to run. If you have never worn compression tights before, though, they might feel overly constricting and a bit awkward at first. But their (literal) tightness is exactly how they can be helpful to the wearer.
There certainly is no wrong time to wear compression tights (except, of course, in situations and settings in which a very laid back and casual attire choice is prohibited or not acceptable). Even if you are taking a break from running, compression tights still offer benefits for your legs and are just all around extremely comfy (once you get used to them). But to get the most out of your purchase, throw on your compression tights after a work out to speed up recovery, in the days leading up to a big run or race to increase circulation to your legs, and when you are traveling on a plane, in a car, or any time you will be seated and unable to get up and move about freely for an extended amount of time.
Obviously, compression tights compress your muscles. When this happens, the muscles need increased oxygen and blood flow. Increased blood flow is exactly what helps the body not only recover from an injury faster, but speeds up recovery after an intense workout. Let's say you challenged yourself to a really tough track sprinting workout. And a few hours after you complete the workout, you really start to feel your quads and hamstrings as they tense up. When you push your body through tough workouts, the muscle fibers are literally being ripped apart so that they can repair themselves and grow back even stronger. But it takes oxygen and blood flow for this repair to happen, and compression tights can expedite the process. And making sure your tired muscles get plenty of oxygen is not only beneficial for healing, but keeps them feeling fresh and less stiff. This means less time has to be spent pre-race warming them up, stretching them out, and getting them ready to run fast.