What does disable BBcode and Smilies mean?

Exactly that, if for some reason the code (if you use it) is getting in your way, it tells the system to ignore it. For example, if you number items in your post like this:

1)
2)
3)
...
then number 8 comes out like a smiley face. With Smilies disabled, it looks like 8)

It's the same with bbcode. Sometimes you want to show people how to use the code. With it disabled, you can type the code and it displays as text. With the code turned on, all you see is the effect of that code. Read the FAQ to understand what bbcode is and how to use it.

Thanks Dave
I did go read the FAQ on BBcode and it did help.

Go up to f.a.q and scroll down to smilies then read.

Smilies are little pictures or emoticons that you can insert in your posts to convey a feeling such

Just under the message reply window there is a comment about smilies with a clickable link. If you want to insert an emoticon, just click on that and you'll get a window with all of available ones and their codes. Simply copy/paste or type that code into you message. The code will automatically change to the picture.

Can you use text formatting at the Magic Café?
Specifically I wonder if [size=16]size[/size] and [color=red]color[/color] tags are permitted.

I'm afraid [size] and [color] tags aren't available. At least right now.