Hmm I am making this up as I go so bare with me:
Outstretch you thumb. Touch the next finger and your thumb nail to nail. It should look like an "OKAY" hand signal or a classy "number 3". The main point is that your fingers make a big circle.
Now stretch your arm a decant distance from your face and place your avatar inside that circle. Try to hold your hand steady on the black spot to the left of the fish eye. I bet you'll notice no matter how hard you try, you can still see your pretty fish head moving up, down, and side to side.
Now take your other hand and make a small circle by touching your thumb and the next finger nail to nail. Place your hand in front of the circle you already have and counteract your shaking hand.
It worked for me but I can see a large margin for error on this example so I'll just try to explain what is going on.
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Your holding the camera but your hands are a little shaky. Inside your lens, the IS tries to predict your shaking and shakes with you. As long as you don't shake too much, hopefully it will counteract your shaking and keep the image on the sensor steady. It can only do so much though.
To accomplish this, the light has to pass through this complex shaking system and you loose some detail along the way. If the image was going to be a blurred mess without it, the good far outweighs the bad. Assuming a 70-200 f/4 and a 70-200 f/4IS were both placed on the same camera on the same tripod in exact same conditions with IS off (even if it isn't doing anything its still there), the subject on the IS lens will be slightly blurred compared to the non IS lens when viewed at full size.
So if you don't need it, IS will degrade the image compared to what it would be without and IS system. Of course the whole reason for having it is that sometimes you can't get a useable image without it. A tripod is the ultimate image stabilizer and works better than any IS system will ever be able to. Sometimes you just don't have a tripod. 75% of the time when hand holding a lens, IS will improve quality more than it will degrade it. With a tripod this is never true. In fact, IS must be turned off on a tripod or the IS will be shaking around with nothing to shake against. The 70-200 IS (both) and the 55-250 IS all know if they are on a tripod and turn themselves off in case you forget. IS also uses battery power at a noticeably faster rate (turning IS off uses no extra batter power).