First time to lead climb

I went rock climbing indoors with my friend yesterday.  I normally top-rope, but he showed me how to lead climb for the first time.  If you don't know, here's the 3 types of climbing that I know of:

1. Bouldering: No harness used, no partner needed, maximum height = 1 story, disadvantage: no rope = no breaks.
2. Top-roping: Harness required, partner needed to belay for you, maximum height = 2 stories, rope is already established for the route, advantage = can take breaks along the way up.
3. Lead climbing: Harness required, partner needed to belay for you, maximum height = 2+ stores, no rope, so you have to bring your own rope and clip it in on the way up.

Lead climbing is harder since you have to hang long enough so that you can clip in.  You have to drag and pull the rope up with you, so that you can clip it into the next one.  Your partner has to pay attention when to give you slack so that you can move up, but remove the slack once you've clipped in.  You're only as secure as the last clip you put in place, so it's scary if you miss a clip or have trouble clipping in- that's where you pray your partner "breaks" (stops the rope), so that you don't fall much.

 

My friend went up first, so he clipped the rope in on the way up.  So my job was to "clean" it up (AKA remove the clips on the way up).  I might be getting the climbing lingo wrong, but I think you can get the gist of it.  My friend clearly stated, "Whatever you do, don't remove the last 2 clips at the top.  I know this sounds dumb, but make sure you don't do it.  Otherwise, your descent will be faster than it should be."  Sounds like common sense, but I think that's why there are 2 clips.