Chris,
Good observation. As you climb, True Airspeed (TAS) increases if indicated airspeed is held constant. By the same token, if one flies true airspeed (which we don't), IAS decreases.
Around 27,000', we stop flying by indicated airspeed and start flying by mach number. This isn't a hard altitude, but generally during the climb there will come a point when we're no longer airspeed limited, but mach limited. The mach number will become the important reference. It's a little easier to visualize on an analog dial airspeed indicator, but there are two upper airspeed limits. One is your max indicated airspeed, and one is max mach. One will be depicted as a red radial line, or other marking, on the airspeed indicator. For airplanes using mach, the mach is a floating pointer generally marked with red stripes, and referred to as the "barber pole."
As one climbs higher and higher, the "barber pole" begins to move down toward a lower speed. The effects of compressibility increase as one climbs higher, for a given airspeed, and the effects of compressibility, or mach effects, become the chief concern. When one first takes off, the airspeed at which the mach limits would occur is much higher than the maximum indicated airspeed, and we pay no attention to the barber pole or mach number. However, as we climb, the airspeed at which the mach limit occurs (easier to think of as the speed of sound decreasing as the air gets thinner and thinner) drops. At first we may have a maximum indicated airspeed of 350 knots, for example, but the mach limiting speed would occur at 400 knots. As we climb, there will come a point as the speed of sound (which is our reference for mach numbers) decreases, we will note that the mach limiting speed is the same as the limiting airspeed...say both now at 350 knots. As we climb higher, we will see the limiting mach number decrease further, and perhaps be 220 knots indicated...that's where the "barber" pole sits. The limiting max airspeed is still 350...but that's of no concern to us because now we're mach limited.
Have you ever gone underwater in a swimming pool and listened to sounds traveling in the water? Sounds are transmitted very well, and move quickly through the water; you can hear the slightest noises from the other side of the pool. The water is more dense. It appears to amplify everything. You try to run, you move slowly. You can feel the water holding you back.
Flying down low is a little like running in the water. You can go to a higher indicated airspeed, but you're fighting thick air. The speed of sound is higher in that thick air. Climb a little, and your indicated airspeed remains the same, but you're really going much faster; true airspeed increases. Somewhat like if the water could magically be thinned to a lesser consistency. As the air thins, the speed of sound decreases; sound doesn't move as fast or as far through the air. Put a block of wood near your ear and tap the other side with a spoon; you hear the sound just fine. Put a pillow by your ear and tap the other side, and you don't hear much at all; the sound doesn't travel through the less dense pillow very well, nor does it travel through less dense air very well. We use the speed of sound as a handy reference number for our mach effects because mach effects are somewhat tied to the same air properties that affect the way sound moves through the atmosphere: density.
For your indicated airspeed, remember that the source for that instrumentation are small tubes, pitot tubes, that sample the air pressure rammed into them as the airplane moves forward through the atmosphere. The faster the airplane goes, the more pressure rammed into the pickup, or pitot tubes, and consequently the higher the indicated airspeed. Imagine if the air were twice as thin (which it is at roughly 18,000')...you'd have to fly much faster to produce the same pressure in the tubes. Which is why to get the same indicated airspeed at high altitudes, the true airspeed is much faster. You're flying faster and faster, but still indicating the same speed. Finally you fly high enough and the air is thin enough that you simply can't pack enough air into those tubes to produce the same indicated airspeeds. You're going fast, but the air is just too thin to register as well.
At this point, because the air is thin, it reacts a little differently to the wing. It's easier to compress or pack together in some areas, such as in front of the wing or nose, and there it forms "shock waves." These shock waves in turn affect the airflow about the wing and the way lift is develop, as well as control features of the airplane. These are mach effects, and the designers of the airplane have determined exactly how far one can go before running into adverse effects. This is the purpose of the barber pole; to keep you away from those effects. It's for this reason that you're mach limited at altitude, rather than airspeed limited.
Indicated airspeed is still valueable, even though we don't use it as our go-fast reference. That is, even though we're watching our mach number for our fast limit, we still closely watch the indicated airspeed for our lower "buffet boundary," or stall. We may be able to get away with a stall at 100 knots at low altitude where the air is thicker and we can make the same lift with a smaller angle between the wing and the wind (angle of attack)...but at altitude, we have to fly faster and perhaps use a larger angle to do the same thing...our stall speed goes up. We may have a stall speed of 160 or 170 knots now. Suppose we're limited to 210 knots due to mach at cruise, and our stall is 170 knots. This means we have a 40 knot window, between 170 and 210 indicated, in which we can operate. The higher we go, the smaller this window gets. Eventually it can get very small if the airplane has enough power to get up that high. That little window is sometimes referred to as "coffin corner," or the place where slowing down any more will cause a low speed stall, and speeding up any more encounters mach effects.
That may be a little more than you wanted, but it's also why as you climb higher and higher the airplane appears to be restricted to slower and slower speeds, and why if you look at an indication of your groundspeed (how fast you're really moving, in relation to the earth) in a no-wind situation...you're really going faster and fast. Clear as mud?