I'll try and put this in other terms. One knot means 1 nautical mile per hour. A nautical mile is longer than a statute mile, hence 100 knots is faster than 100 mph. This ratio remains the same as others have said.
I think your confusion lies with indicated airspeed (IAS) vs. ground speed. If you climb at a constant IAS of 250 kts. in calm wind for example, your ground speed will increase as you go higher. This is because as you climb, you pitot tube, which measures ram air pressure and delivers that information to your airspeed indicator, begins to move through less and less air. Its easy to maintain a constant IAS, however, because your airplane will move faster through the thinner air and keep the same volume of air entering the pitot. If you takeoff on a runway that is at 5,000 ft elevation, your airplane will move across the runway at a higher speed than when taking off from a runway at sea level (assuming standard atmospheric conditions), yet you IAS for rotation and takeoff (generally speaking) will always remain the same.
So when you're on an airliner, your airplane may be cruising at 250 kts. IAS, but your pilot may announce a ground speed of something like 600 mph.
It's actually hard to explain but I hope I did a good job.