I feel this game wasn't over because white was ahead... Can someone explain why my opponent resigned?

Hi barraktu, you would have to ask your opponent.
At these levels, had the game continued, nobody knows who would've won.

The upper left corner: study this joseki --
your connect looks very solid, but it's not joseki --
there are other variations, but study this basic one.

Every move in this sequence has its meaning.
See if you can figure out why the joseki move is extend, and not your solid connect .

My best guess would be that the extension instead of the solid connection is to stay ahead of the opponent and keep them sealed in the corner. In the game I made a solid connection because I was afraid of the cut on 15-D. But looking at it now, the cut doesn't seem as severe as I thought and trying to cut would have let me take away more of the corner territory. Thank you for the reply, I will try to get in contact with my opponent again.

Good, but we're not done.
Let's study the joseki SGF in Post 2, to keep things simple.
Two homework problems for you:
- If B does not extend on , if B tenukis, then what is W's follow-up sequence ?
- After extends, what happens if W cuts D15 ( instead of ) ?

I'm pretty sure white's next move would be at C-13 after black tenukis. And I think after white cuts black can either push into white's corner or net the cutting stone.

OK, and then ? That's a start, but a single move is not enough:
what is the sequence ? Please show your sequence, with a diagram or SGF.

OK, what are the exact sequences.
Please show with a diagram or SGF.

I couldn't create the file correctly. But, In both scenarios I imagine the sequences would go as such:
B D-16 -
W - C-17
B D-17 -
W - C-16
B C-15 -
W - B-15
B C-14 -
W - B-14
Sequence One
B Q-4 -
W - B-13
B C-13 -
W - B-11
End Sequence One
B C-13 -
Sequence Two
W - D-15
B E-15 -
W - D-14
B E-13 -
W - D-14
B E-13 -
W - E-14
B F-14 -
W - D-13
B D-12 -

Good time to learn How to make Diagrams .

Also, good to figure out what happened to your SGF attempts.

Here's a start: you can use it as a template —
just click the button "quote" and edit as you wish:

Click Here To Show Diagram Code

[go]$$B tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X . . . . . . .
$$ | . O X . . . . . . .
$$ | . . 2 . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .[/go]

Right — in your variation above,
is self-atari, so W would not play it.

So nets the two stones:

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X 2 3 . . . . .
$$ | . O B 4 . . . . . .
$$ | . . 1 . 5 . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

Which means there is no cut at after extends,
which means the two extends, and , are a more efficient way
to fix the cut than your solid connect .

The other homework problem: what happens after ?

Click Here To Show Diagram Code

[go]$$B tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X . . . . . . .
$$ | . O X . . . . . . .
$$ | . . 2 . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .[/go]

This one is interesting to me. I'm no sure if I get it.

You are very, very scared of cuts. (Probably because some players cut you into pieces and you died many horrible deaths ? )
The solution is not to connect every single cut as soon as you are worried.
Rather, strive to improve your reading and fighting skills.

B would hane at — and then ?

Click Here To Show Diagram Code

[go]$$B tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X . . . . . . .
$$ | . O X . . . . . . .
$$ | . . 2 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .[/go]

Would it be something like this?

W would double-hane at — and then ?

Click Here To Show Diagram Code

[go]$$B tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X . . . . . . .
$$ | . O X . . . . . . .
$$ | . . 2 3 . . . . . .
$$ | . . . 4 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .[/go]

Isn't it interesting how much one can tell about a person from just two moves —
connect in post 1; and connect in post 14.

It's so bad to allow white the hane at 2 I'm not sure what's best, but this falling back might be better shape.

Click Here To Show Diagram Code

[go]$$B tenuki
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O X . . . . . .
$$ | . . O X . . . . . ,
$$ | . O X . . . . . . .
$$ | . O X . 3 . . . . .
$$ | . . 2 . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .[/go]

It would seem that the best move is to simply follow the joseki rather than deal with the consequences of trying to be fancy.