Why are planes slower at higher altitudes?
This is because what you are looking at is the IAS indicator (Indicated Air Speed).
This represents the amount of relative air which flows over and under the wings of the plane. This is what creates lift and enables the plane to fly. This is why this instrument is so important and belongs to the primary flight instruments.

This is not to be confused with GS (Ground Speed), which can be sensed by IRS (Intertial Reference System), or by the GPS. Ground Speed is not relevant to pilot an aircraft, but it's still useful for example to determine the ETA (Estimated Time of Arrival), and for fuel estimation during flight.

The IAS indicator indicates a lower speed because the more you climb, the less air there is. So even the air flows faster, the global pressure feeling is lower.

So, actually planes are not slower at higher altitudes. They are faster (at least most planes whose flight envelope force them to fly faster when they are higher, otherwise they would stall, because they would have to increase their Angle of Attack too much to counterbalance the lack of air flowing above and under the wings). But when they reach their target Mach speed, their speed will decrease slowly as the outside air temperature is decreasing until end of climb.

Sorry for the picture being in French... But as you can see, the flight envelope of an airliner forces him to actually fly faster as it is climbing.



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Different speeds

There are different speeds on an aircraft, and it can be quite confusing.


IAS (Indicated Airspeed) is what the instruments directly sense. It is computed by subtracting the static pressure (static ports are placed on the fuselage, vertically to relative airflow) from the total pressure (pitot tubes are placed parallel to relative airflow. This gives a measured dynamic pressure which is then displayed in knots, km/h or mp/h. This speed is showed on most general aviation aircrafts as the main speed indication (but it's actually not a speed and more a 'pressure of air feeling').
CAS (Calibrated Airspeed) is the same as IAS, but without instrument errors. It gives a speed related to the real dynamic pressure felt by the aircraft. This speed is showed on most airliners as the main speed indication (for pilot and autopilot).
TAS (True Airspeed) is the same as CAS when at 15°C, 0% humidity, 1013,25 hPa (29.92 inHg) (ISA, International Standard Atmosphere). This time it is literally the air speed (speed of the air): it is the real speed at which the relative air flows around the aircraft. It takes into account the fact that air density is not always the same. This speed is used when measuring or referring to an aircraft performance during cruise for example. It is also used during flight planning before the wind has been taken into account.
GS (Ground Speed) is the speed of the aircraft relative to the surface of the Earth (the equivalent of the speed showed in a car). In an airplane, we cannot use wheel speed to measure it because we are in the air, so we need GPS or IRS to do this. If there is no wind outside, TAS and GS are the same. If there is 30kt tailwind, GS is 30kt higher than TAS. This speed is used to know when you will arrive at your destination airport, and to know if you will have enough fuel (because the wind is taken into account). This speed is also used when the aircraft is on the ground (when taxiing, or more generally at low speeds when wheels are on the ground). Airlines or airports fix speed limitations when taxiing. The only way to know if you respect the limits is to look at the Ground Speed. Also, the airspeed indicator usually won't be active below a certain speed (45KIAS for the B737).


So, why is the primary airspeed indication (IAS or CAS) the wrong speed (not actual speed) of the air flowing around the aircraft?
This is because this wrong airspeed represents actually the real pressure feeling around the wings that is responsible for the lift. It is this parameter that we need as pilot and it is used in aircraft manuals to describe the V-speeds. It's perfect that IAS and CAS are not corrected with altitude and temperature, because if we know that our airplane stalls at 120kts for example, we won't need to care about altitude or temperature. Our airplane will stall at that same speed regardless of altitude and temperature. If we would use TAS, stall speed would be constantly changing and it would be more difficult to keep the aircraft in good and safe flying conditions.

  

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Here is where you can find these speeds in the Boeing 737 NG cockpit: