Alginic acid is a simple polysaccharide. What makes it neat is that it will form gels in the presence of divalent cations (e.g., calcium and magnesium).
It's useful anywhere a biocompatible and/or edible gel is required - one well-known use is fake cherries. If you drop a solution of sugary, red, cherry-flavored sodium alginate into a calcium-containing solution, the exterior of the droplet will skin over and form a gross little cherry-like thing.
Interestingly, the famous "molecular gastronomy" restaurant El Bulli uses alginate extensively to create caviar-like droplets of various liquids. I think it really sounds like a neat idea and I'd jump at the chance to eat there, but I think one problem with "molecular gastronomy" is that some practitioners get caught up in some of the gee-whiz tricks they can do with some additives you find in your twinkies anyway. Lots of the stuff at EB sounds great, on the other hand...
This entry made me smile. I remember playing with this stuff back in school, immobilising enzymes in biology lessons. There were slimy little grey blobs all over the lab by the end of the day.
I understand that El Bulli closes for six months each year. The staff goes offsite to their lab and experiments for the six months developing the new recipes. Heck of a business model!