what is this and what does it do?
 

I have an 06 S60 2.5T, and recently I noticed this hose was broken in a couple of places.

That's the breather hose and it's part of you PCV system. It goes to the breather box/oil separator under the intake manifold. Yes you should replace it sooner then later.
Part# for that piece alone is 8692217, but depending on your miles, it might be a good idea to replace the whole system.

EDIT:
Here's the whole system...
http://www.ipdusa.com/products/4991/...c70-xc90-turbo

And just the breather hose its self...
http://www.ipdusa.com/products/6612/...-breather-hose

If I wanted to replace the hose myself, would it be a difficult job? I have moderate skills, but I'm somewhat limited as far as tools go.
Or, is this a job best left to a professional?

Not sure how hard the job is on a S60 but on the 850's it take the pro's about 2-1/2 hours and 5 hours for DIY'ers. The entire system should be replaced.

Look for instructions on your model car and decide if you'll do it yourself or pay to have it done.

The hose it's self took me a little over an hour to replace without taking off the intake manifold. But I did the hose only because I had low mileage at the time.
I would replace the whole PCV system and have the pros do it since the intake manifold needs to come off. It's not really all that hard, just very time consuming. Get the PCV system from the link I provided in my first reply and have an indie shop do the work. It'll save you a lot of money over the dealer.

An indie shop will probably charge you for 4 hours of work, so make some calls to different shops - and make sure they know Volvo engines!

There's a great post over on MVS that I used to do it myself. It can be frustrating, but you don't need to be an expert mechanic to tackle the job.