Electricity generators capacity question?

Electricity generators often state their capacity in KW or MW. But, is this per hour, per year or per what? Eg- Generator capacity 200MW. Is that 200MW per hour?

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Electric generator capacity is stated in KVA, or kilovoltampere, not KW.

KW or MW applies to the mechanical load the prime mover, turbine or engine, can carry.

These are instantaneous values, i.e., the load it can carry continuously.

MWh is the MW power delivered during one hour, which is not power but energy.

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Power is energy used/unit time. So a generator rated at 1 MW produces 1 million Joules of energry every second. It does this for as long as it is running. How long it can continuously run depends on many factors - mechanical design, workmanship, etc.
You are confusing Energy with Power.

Power is the rate at which Energy is delivered.

That 200 MW generator will generate 200 MW-hours of Energy in one hour if it runs for 1 hour, and the load is 200 MW steady for 1 hour.

If there is only a single 100Watt light bulb attached to that 200 MegaWatt generator, then it will only put out 100Watts. At that rate it would take over 228 years for the geneator to produce 200 MW-hours of Energy, because the light bulb doesn't use Energy at a very fast rate, compared with a small city that would use up that much in 1 hour.

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The wattage rating of a "generator" (most are actually alternators) is an instantaneous load rating. For exaple, a rating of 2000 watts means it can supply 20 one-hundred-watt light bulbs continuously.

A generator rated at 10 KW can supply 10 KW continuously, or 10,000 watt-hours per hour, if you want to think about it that way.

Most generators have a peak overload rating, usually about 150 percent of the load rating for two minutes or five minutes.
KW stands for kilowatt. If you have 120 volt power in your house, which is standard in the US, and you have a space heater which is a 1200 watt heater that means that it uses 10 amps of power. This is determined by the formula Volts x Amps = Watts. If you ran the heater for one hour it would use 1200 Watts or 1.2 KW. The KW rating is the maximum that the generator could power in one hour.
The rated capacity is for maximum continuous output - until they are taken off-line for maintenance or fail for some reason. In the case of nuclear reactors, this output can be maintained for years. Consumer generators may give two different ratings; one for continuous output, the other a peak output (slightly higher and not to be maintained for any great length of time).

We are billed by our utility for kilowatt hours - this includes time and is a factor in how much work was actually performed. Any generator will actually vary its' output based upon the load connected to it (at least up to its' rated load).

Best regards,

Jim