Need Education on Compact Double verses Triple

[Cyclesome]

I recently purchased a Specialized Ruby with a Compact double cassette 50/34. How does this compare to my triple cassette on my Cannondale hybrid which is 28/38/48? Will I be able to climb hills with my compact double? My Ruby is as light as a feather compared to my 30 lbs. Hybrid, but will I have the gears necessary for climbing? I took my Ruby out yesterday and road her for 25 miles, but didn't tackled any huge hills.

I need a basic 101 explanation of these gearing systems. Sorry if I appear unknoweageable, I am still in the learning process.

Thanks!