The browser works and can do some decent things, but it really isn't all that amazing. No flash and no HTML5 make it pathetic. No tabbed browsing/new windows, and with the lack of multi-touch, a horribly limiting zoom (although they could have found a work-around, but I guess that was too much trouble).
It can run javascript though (kind of obvious). Someone has already started with web-based apps for the 3DS:
http://www.youtube.com/watch?v=yOdBgTShd3k
You can try it out on your 3DS by pointing the browser to
http://3ds.andysmith.co.uk/jFox.html
It's functional, but nothing amazing. I don't think GBATemp likes linking to other sites (too late, I guess) so just in case, I won't link to the interview with the guy who made this (Andy Smith. Duh), but the guy said that the D-Pad and A button are fully functional in the browser, hence why this was possible, but that it uses the scrolling function of the D-Pad to act as a control for the game, and therefore can't use the top screen (you can try, but it'll move to the bottom screen as soon as you press the D-Pad). Something like that, anyway. He also said that so far, sound isn't possible, what with the lack of Flash and HTML5.
Other than that, I don't really care. I'd much rather use my iPhone or a computer. The 3DS browser seems slow, clunky and fairly featureless to me.