The exact number on an EGT gauge is usually meaningless: The Alcor EGT gauge you'll find on many aircraft has no temperature markings on it - just 25-degree divisions, and a yellow "reference pointer" which the pilot sets to the maximum observed EGT:
The notable exception to this is turbocharged engines which have a Turbine Inlet Temperature (TIT) limit to protect the turbocharger. For engines with exhaust gas / turbine inlet temperature limits these limits will be specified in the aircraft's Pilot Operating Handbook, and usually marked with green/yellow/red arcs on the relevant gauges.
Exhaust Gas Temperature (EGT) provides pilots a way of monitoring the fuel/air mixture in the engine. It uses the stoichiometric mixture (where Fuel and Air are perfectly balanced so that there is no unburned fuel and no unburned oxygen at the end of the combustion event) as a reference: At this mixture the EGT is at its hottest ("Peak EGT"). Making the mixture richer or leaner will reduce the EGT, and all other mixture settings are described in terms of "Degrees Rich of Peak" or "Degrees Lean of Peak".
Refer to the handy chart from Lycoming below for the remainder of this discussion:
EGT and Mixture
When we talk about mixture in piston aircraft engines we're generally interested in one of two things: Best Economy - getting the most power from the engine for the least amount of fuel, or Best Power - Getting the most power from the engine regardless of fuel burn. We're also interested in something called Detonation Margin, which in simple terms means "how likely is this mixture to explode rather than burn nicely?"
As you can see on the Lycoming chart above the EGT provides us a way of finding those mixtures.
Best Economy Mixture
The "Best Economy" range begins at peak EGT, and continues on the lean side until the engine won't run smoothly anymore (usually the limit is about 100-150 degrees Lean of Peak).
Operating the engine at Best Economy mixture provides the most power for the least amount of fuel, and thus the longest endurance. It comes at the cost of a reduced detonation margin on the fuel/air mixture - operating at high power settings with a best economy mixture increases the chance of detonation.
Most aircraft/engine manufacturers recommend Best Economy mixture for power settings below 75%, in part to reduce the risk of detonation.
The Red Box - Where you don't want to run your engine.
The area of the chart from peak EGT to about 100 degrees Rich of Peak is often referred to as "The Red Box" -- in this range the fuel/air mixture has a low detonation margin, and the combustion event is producing the most internal stress on the engine components (cylinders, pistons).
As you can see from the Lycoming chart the Cylinder Head Temperature (CHT) peaks in this range, and there is a risk of exceeding the CHT limits and seriously damaging your engine by operating in this range for extended periods of time, particularly at high power settings.
Best Power Mixture
From approximately 100 degrees Rich of Peak to 200 degrees Rich of Peak is the "best power" range - in this mixture range you can safely run the engine at high power settings (from 75% of rated power to full rated power) with limited risk of detonation. The engine is producing the most power it can in this range, which is useful if you need to climb over an obstacle in your flight path.
For simple aircraft with fixed-pitch propellers the "Best Power" mixture can also be found by adjusting the mixture to obtain maximum RPM for a given throttle setting.
Operating in the "Best Power" range is not without risks - in particular, detonation is still possible at high power settings. The same Lycoming manual that I pulled the chart above from advises monitoring CHTs when using Best Power mixture settings.
Less Interesting Mixtures
There are two ranges on the chart I did not discuss above - they are what I call the "Less Interesting Mixures"
Leaner than Best Economy
As you continue to lean the engine past the "Best Economy" range you will notice a sharp drop-off in power. This drop is so precipitous that you will no longer be saving fuel as you leave the Best Economy range: You will be burning more fuel per unit of horsepower produced than you were in the economy range.
Eventually the engine will run rough as the mixture becomes too lean to burn, and at the very extreme end the engine will quit, starved of fuel.
Richer than Best Power
Mixtures richer than Best Power don't produce the same precipitous drop in horsepower, but they consume substantially more fuel per unit of horsepower produced. They also have other negative side effects, like producing black sooty exhaust that will get all over the belly of the aircraft.
As the mixture gets richer it will eventually become too rich to burn, and the engine will begin to run rough as it did being leaned. At the far extreme the engine will become flooded, and cease to run.
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