The [[url=http://[/URL]="http://en.wikipedia…"]Wikipedia[/]="http://en.wikipedia…"]Wikipedia[/] explains it well.

A peak sensing compressor responds to the instantaneous level of the input signal. While providing tighter peak control, peak sensing might yield very quick changes in gain reduction, more evident compression or sometimes even distortion. Some compressors will apply an averaging function (commonly RMS) on the input signal before its level is compared to the threshold. This allows a more relaxed compression that also more closely relates to our perception of loudness.

Drums signals are going to have a higher peak level than an RMS equivalent pad or bowed string.

Also because RMS level is a root mean square average over time, the peak level detection will have a faster attack at the cost of some distortion.

Ah yep
RMS is the Root mean square,

To simplify things you can think of the rms level as a average level. Say you have 3 bank accounts. Each bank account has 3 different amounts of money.

Say:
Bank 1 = $40
Bank 2 = $50
Bank 3 = $60

The average amount of money per bank would be:

(40 + 50 + 60) / The number of Banks (3) = 150/3 = 50

Now the rms value is a bit different calculation:

The rms average amount of money per bank would be:

((40^2 + 50^2 + 60^2) /3)^(1/2) = ((1600 + 2500 + 3600)/3)^(1/2) =2567^(1/2)

=50.7

Peak is the largest value. Either negative or positive. In electronics you will hear the term peak to peak. Think of a sine wave swinging around 0V. The distance from the OV mark to the crest, be it negative or positive is the peak value.
Check this link for pretty pictures:

http://ourworld.compuserve.com/homepages/g_knott/elect39.htm

In Simple Math ->
You can convert overall peak values to overall rms just multiply by 0.707 =(1 /root 2).

So.... in peak mode your compressor looks for peaks to act on. usefull for catching quick transients, tameing a ACU GTR for example. Peak compression when used with a large ratio and slow release times will be more noticeable. In this mode the RMS filter in the control path is removed.

In rms mode the compressor responds to changes in the rms level.
The overall level will be smoothed out. In this mode the rms filter in the control path is engaged, and the control signal (either the input (feedforward) or output (feedback)) is changed into an rms level. This dc level then controls the amout of attenuation in the gain control device (Typically a VCA or optical device).

Hope this helps.