Trying to purchase a thermostat for electric baseboard heat.

Short answer: It means that the following relationship is true:

Power in Watts = V in volts Volts multiplied by current in Amps.

Example: A 2400 W heater at 240 V draws 10 amps.

The relationship is valid for Electric baseboard heat.

The thermostat is basically a switch.
There are three electrical loads as far as switches are concerned. The easiest on the switch is called resistive. When you turn the load on it comes on drawing more or less it's rated load, and when you turn it off it's off.

Next is inductive, typically consisting of motors and transformers. Turning this on is no problem to the switch, but when turning off the magnetic fields collapse in the inductive elements causing arcing across the switch contacts, degrading the quality of the contacts and shortening their life.

The third load is called tungsten. When you turn on a cold incandescent lamp the current for the first fraction of a second is about 10 times what it will be when the bulb warms up. This current may be enough to weld the switch contacts together.
Switches have design elements to handle these conditions which may shorten their life.
"Resistive rated" means use the switch for baseboard (resistance) heaters if you want long life from it.

While the answer above is really good, I will correct a part of it.

Large current draws can occur in inductive loads depending on where in the cycle it happens to turn on. The voltage across an inductor cannot change instantaneously, thus initially the inductor acts like a brief short. Thus, for a 240 V system the switch could see (240*sqrt(2)/2) volts into a brief low resistance.

You can go on and on about loads. Resistive and inductive matter. I could add metal halide lamps, arc lamps or fluorescent lamps to this picture too.

So if the thermostat is resistive rated, it will last longer if I am using it for electric baseboard heat because the heaters are a resistive load?

No, resistive rated loads are appropriate for baseboard heating primarily because of cost considerations.

The same rating switch for an inductive load would be labeled in HP or horsepower. There are 746 watts in a HP, but you cannot use that number to size a switch in amps. e.g. I = 746 W divided by 120 V. It must be rated higher. Usually switches designed for this purpose have a rating in amps and HP.

Thanks K.I.S.S.

Your welcome.

Here is a data sheet that will make your head spin:

http://www.automationdirect.com/static/specs/eatoncontactors.pdf

The CE15AN is a contactor (a special kind of relay) which has a 20 A rating when used for resistive loads and a 7A rating when not. Furthermore, this particular contactor has different ratings depending on what it's used for, the voltage and phase.

I tried to distill it for you, now you might be in a position to understand it.