What does this thing mean? Please help a noob...

Ok, so I am a total FCP nOOb. I am pretty much learning everything by watching tutorials and reading articles. I get the basic gist of it and have made a couple short movies. The problem I'm having is that I'm getting random frames of other clips appear in my movie. I've noticed that the ones that are showing up are marked with a symbol that I have searched high and low to find the meaning of. What does this marker mean?

That mark indicates that you are at the first frame of your clip. Hit the back arrow and you will see that you will now be at the last frame of the previous clip.

Ahhh, k. Any idea why random frames would be popping up further down the timeline? I can't even see them to actually select and delete, they only show up when I'm skimming or playing. If I delete all my clips, I see a tiny lil sliver of the frame that is causing havoc. I've noticed this happening mostly when I add transitions/titles.

Yes, that is usually when they can happen. If you don't have enough media at the start or end of a clip for a transition, FCPX will create an overlap transition and will put a segment of the clip at the end or further down the timeline. There are other things that can sometimes cause this. Expand your timeline as large as you can and you will find the offending sliver of a clip. Select it and delete it. When editing, make sure you have enough handles each side of the clips to properly place a transition.

Spend a few bucks on Michael Whol's FCP X course at macProVideo or Ripple or Apple Pro Training Series book, and just be up to speed right away. You'll be very glad you did.

And be sure to check out the tutorials posted here.

But those trainings I suggested actually teach workflow, best practices, etc. Very well worth the time and investment. You'd be amazed.