KIAS means 'knots indicated airspeed'. A knot is a nautical mile per hour.
KIAS is one of the speed units used in aviation. There are several others: rectified airspeed (RAS), true airspeed (TAS), and ground speed (GS).
KIAS, or indicated airspeed, is the basic, most crude measure of airspeed. That doesn't mean it makes "your mom" jokes all the time. It's the measure of an aircraft's speed through the bit of air it's flying in.
Why is this crude? Because it ignores a) the aircraft's speed relative to anything useful, b) movement of the air itself, and c) the properties of the air. What this means is that KIAS is almost always wrong as an indicator of aircraft performance.
For instance, imagine an aircraft with an airspeed of 75 knots. Simple enough? 75 knots across the ground? Wrong. Turns out that it's flying into a 75 knot headwind. So amusingly, the aircraft is actually stationary relative to the ground. Its airspeed might be 75 knots, but it's not going to fly 75 miles—or any distance at all—in an hour. Unless you count the 75 "miles" of air that have rushed past it.
So how about air properties? Well, all measurements of anything are taken against a known and agreed baseline. Air pressure is measured in standard units, and that measurement is compared to a known standard, or scale. The only way the reading has any meaning is by comparing it to this standard. The speed given by a KIAS dial is the aircraft's airspeed, assuming it is at sea level, flying in the conditions of the ISO Standard Atmosphere, which amongst other things lists air temperature (15°C) and pressure (1013.25 millibars/29.92 inches of mercury). All of these things affect airspeed readings.
As you might know, as a general rule if you increase your altitude, the temperature, pressure and density of the air around you decreases. There are fewer air molecules in a given volume of space than there are at a lower altitude. The air is thinner. Airspeed is a measure of dynamic pressure, which is calculated as the difference between static pressure—the pressure of the air around the aircraft—and stagnation pressure—the pressure created by air hitting the aircraft (strictly speaking, the air entering the aircraft's pitot tubes, which are used in measuring airspeed). At a set speed, the pressure of air hitting an aircraft varies with its density. This can be affected by altitude and/or temperature.
So if you maintain a constant speed across the ground and climb, your KIAS will decrease steadily as you do so. The air is getting thinner and its pressure on you is decreasing, so it is having less of an effect on the airspeed indicator's mechanism. Conversely if you descend from high altitude, to maintain the same KIAS you would have to decelerate.
Air density also affects your lift. Wings have to displace a certain amount of air in order to keep you aloft, and if they're going too slow through the air to do this they stall. The critical airspeed, below which this happens, is the wing's stall speed. As you climb, the density of the air decreases, which means that you have to accelerate to get the same amount of lift from the wing.
Although KIAS is almost always wrong as a measure of aircraft progress over the ground, the conditions affecting it—instrument error, errors induced by the position of the pitot tubes on the fuselage, errors induced by compression of air as it hits the fuselage—can also be measured, so true airspeed can be derived from it.
One further, interesting thing to consider here is mach number: the ratio of your speed to the local speed of sound (e.g: mach 0.8 is 80% of the local speed of sound). I say 'local' since the speed of sound also changes with density; it travels more slowly through a less dense medium. For instance, in air at sea level, at 20°C, the speed of sound is about 767mph. In water—which is about 800 times denser—at the same temperature, the speed of sound is over 3,000mph. By contrast, in the low-density air of high altitudes the speed of sound is more like 660mph.
However, although the speed of sound varies with altitude, the behaviour of the air at different mach numbers is generally the same. So at high altitude, aircraft tend to navigate using mach number rather than any of the other measures of speed that exist. This has an interesting effect on commercial airliners. They are generally, with a couple of exceptions, not designed to exceed the speed of sound, although a few have by accident. All aircraft designs have a critical mach: a mach number they are not designed to exceed. Doing so can result in severe buffeting and possible structural damage. Fair enough, but the speed of sound decreases as you climb, right? Airliners are pretty big, and they need to fly fast to stay aloft in thin high-altitude air. See, this is why computers fly airliners these days: it's a bit of a balancing act. The window of speeds that are 'available' at cruising altitude is generally quite small: much lower, and you'll stall and fall out of the sky (albeit with a pretty good chance of recovery); much higher, and your wings will fall off and then you'll fall out of the sky. Pilots sometimes call this narrow envelope 'coffin corner'.
As another interesting aside, consider the SR-71 Blackbird, the fastest and highest-cruising jet aircraft ever made. Although many of its specs are still classified, commercial simulations like FS and X-Plane suggest that the stall speed of the SR-71 at its cruising altitude of ~80,000ft is well over mach 1. It had to exceed the speed of sound just to stay in the air.
So anyway, to summarise, KIAS is often inaccurate but you need it as a starting point to calculate the other, more useful airspeeds like rectified airspeed and true airspeed. But above a certain level (this level is decided by air traffic control for the area in question) we switch to mach numbers for measuring and controlling aircraft speed.