In essence, an inversion is a Yoga pose that turns you upside-down to some degree. Common examples are headstand and shoulderstand, both of which I'll talk about more in a moment. However there are plenty of simpler gentler, and safer ways to invert, and they give many of the same benefits.
Benefits and Cautions
Our bodies are mostly water, which is constantly affected by the pull of gravity. When we invert, gravity is now pulling the other way. The stale blood in the legs returns more easily to the heart whilst the brain gets an enhanced supply of oxygen. The lymph system removes waste products more efficiently. You might find relief from blocked up lungs, and indeed all the organs can be affected.
However this reversal is not guaranteed to be beneficial for everyone - consult your doctor if any of these apply to you or if you are in...