Can anyone explain this in laymans terms?

Compact refers to the size of your chain rings (the gears if front).
STD in general is a 53/39 (no. of teeth on the ring)
Compact will be like a 50/30

The smaller rings mean your largest gear is lower but your lowest gear is about what you find on a triple

Current road double cranksets are typically 53/39 rings on a 130 or 135BBCD crank. Compacts use a 110 bcd and typically 50/34 rings or sometimes a 36 to get lower gearing wthout going to a triple,and without giving up much on the top end. A triple will give lower gearing if that is what one really needs, due to the use of an even smaller granny ring.

It's usually 50/34 for the compact. Smallest ring you can use is a 33T.

wrong.....it's typically 50/34.

Was just wondering, because I have one on my new bike (Giant TCR2) - a Truativ, but it feels pretty similar to my old 42/53 - am I just imagining it?

What kind of casset do you have on it?

If you have a 11-23 cassette you can get a pretty good speed range out of the little 34 ring becasue the cogs are 1T smaller at the end of the cassette compared to one that begins with a 12T.

In other words a 34-13 is only a tiny bit shorter than a 39-14. (both are 3rd smallest cog in the cassette)

The only negative I can really see is that the shift into the smallest cog is slightly larger percentage-wise going from a 12T to an 11T compared to a 13T to a 12T. In reality though this isn't noticeable. Although a 50-11 is a much larger gear than a 53-12.

Included a Picture, cropped a bit to fit. Look at the size comparison in the lower RH corner (check out the Road Components!)

Compact cranks have a smaller bolt circle diameter so you have the option to fit smaller rings.
There are 2 uses for smaller rings:
To lower the gear ratios so you have a more useful, lower range.
To reduce the weight and give you the same gears with smaller tooth counts (and increased wear)