It's almost exactly like UV resin... but, in either case it's not melting it, rather creating a polymerization reaction where the light gives enough free energy to cause the molecules to react and bond to each other, which typically doesn't require a lot of power. In the case of the body, collagen is a long chain of polypeptides (protein) and is naturally created by polymerization (as many things in the body do), so having something that will cause that reaction without the body's help is very useful. It's a brilliant idea and the guy that created it definitely deserves some recognition for taking two things that a hospital (at least some bigger ones) already probably has and using them in a completely novel way.
The big deal about this, as mentioned in the article, is much tighter/secure sutures. This not only produces less scarring, but really the biggest thing is prevention of infection. One of the biggest problem with surgery is infection because even though we go through great lengths to maintain a sterile field during, afterward the patient is just put back out into the (very) non-sterile world with only those sutures protecting your insides from the countless organisms just waiting for a chance to get in. And, although it may be surprising, hospitals are one of the easiest places to get an infection (called nosocomial infections), so anything that can make you less susceptible to getting one is certainly worthwhile.
You also have the added benefit, like they mentioned, of being able to suture previously difficult things like nerves and delicate areas like your eye which do not take well to regular suturing. If you ever have to have eye surgery where they have to suture the side of your eyeball, you'd probably be very happy to rather have them just smear a little dye on there and shine a laser versus take a sharp needle to it and sew it shut.
The only problem would be the capability of the light to penetrate tissues to bond the deeper areas. Of course, you could find a wavelength of light that does have good (or better) penetration then also find a compound that will act similarly using that wavelength light, but that may be quite a challenge... at least now we know what to do and have exactly what is needed, the only issue is access (that and FDA approval).
