Sure.

The 1s,2s,and 0s are references to the different tiles in the map.  The For loop(s) then display either a single character, or a group of 6 characters in the string example.  Basically the For loops let the sub( put the characters on the screen.

I'd recommend learning about the sub( command.  It's very important when dealing with strings, which happens quite frequently.
http://tibasicdev.wikidot.com/sub

Edit: Here's a more in depth explanation with the matrix:
:[[1,2,1,2,1,2][2,0,0,0,0,1][1,0,0,0,0,2][2,1,2,1,2,1->[A]          //Store the tile data into [A]
:ClrHome           //Clear the homescreen
:For(A,1,4            //This will loop 4 times, making A = 1, 2, 3, and 4 as it adds one to A each time
:For(B,1,6            //This loops 6 times and changes B
:Output(A,B,sub("=87",1+[A](A,B),1                   //This displays a = if the corresponding spot in the matrix is zero, a 8 if the spot is one, and a 7 if the spot is two.  It places it at a spot relying on the values of A and B.
:End           //Ending the For(B loop
:End            //End of the For(A loop

Does this help?

Edit x2: Meishe, ninjas are quite frequent when 5 people are viewing a topic.

Welcome here!

This is an awesome place to learn about the calc.

I need to play those too...

1: You can create a map with a matrix, list, or string.  Here's an example of each method (note that I'm using only 4*6 maps):

Matrix:
:[[1,2,1,2,1,2][2,0,0,0,0,1][1,0,0,0,0,2][2,1,2,1,2,1->[A]
:ClrHome
:For(A,1,4
:For(B,1,6
:Output(A,B,sub("=87",1+[A](A,B),1
:End
:End

List:
:{1,2,1,2,1,2,2,0,0,0,0,1,1,0,0,0,0,2,2,1,2,1,2,1->L1
:ClrHome
:For(A,1,4
:For(B,1,6
:Output(A,B,sub("=87",1+L1(6A-6+B),1
:End
:End

String:
:"8787877====88====778787->Str1
:ClrHome
:For(A,1,4
:Output(A,B,sub(Str1,6A-5,6
:End

Once these are all ran you will see
878787
7====8
8====7
787878

I think this showed how to make a map.

I think Meishe answered the others very well.

2. Matrices, from what I understand so far (I'm not an expert like some of these guys), is one way of storing data for a map. I'm sure there are other uses but that is what I know.

3. Can't help ya there.

4. Yes, if you push [2nd][ + ][2][7] you can see how much memory each program takes up. RAM is your unarchived stuff (the stuff without a asterisk next to it) and you can run that directly. Archived things (archive is a much bigger piece of memory in your calculator) are things you need to un-archive first. In that screen you can just push enter to archive/un-archive programs.

5. Well there are a few things that go into that. There is setting the dimentions for the list and then the actual data. Both of which are found here. They do a lot. Store highscores, saved games, items, maps, etc.

6. Strings can be used for a lot of things too. Mostly, from what I've seen, for making maps and storing text.

I think this is the program you're referring to, right?
http://ourl.ca/4250

Builderboy, I'm also curious.  Could you explain what each little section does so it makes sense?
Builderboy is also the programmer of Peggle, another awesome physics game.  It's in Basic, but I'd still recommend looking at it.
Peggle: http://tibasicdev.wikidot.com/archives:peggle

Builderboy, you're really good at programs like this. Do you mind sharing your methods?

Ah, my bad. 

It's still cool.

That's really cool!  I can't wait to play SAD!

Quigibo, can you compare the code side by side so we can see how to optimize with Axe?  Thanks!
(The Optimization Tricks file is nice, but it can help to see it more. )