OK, here we go:
What is litigation? Essentially, legal proceedings before a Court or tribunal between parties seeking to enforce their legal or equitable rights. In other words, the resolution of a dispute between parties. Or if you want to simplify it any more - companies suing each other. All those cases you study (or will study) in tort, contract, equity, trusts etc have all come about by individuals or corporate entities being in a dispute with each other which has been ruled upon by the Court. Litigation lawyers represent those parties. The vast majority of the work is done behind the scenes rather than in Court. A normal piece of "big ticket" litigation run by a City litigation department might take 18 months to come to trial (and often longer) - the trial is the culmination of months of hard work collating evidence, interviewing witnesses and preparing the case. Many cases settle well before it is heard by the Court. That is especially the case in the UK where legal fees are so high.
Many City firms have "rebranded" their litigation departments as "dispute resolution" departments to reflect the fact that much of our work now involves the use of other procedures to resolve disagreements and disputes between our clients - those procedures are typically mediation, early neutral evaluation, arbitration etc.
A couple of people asked about which Uni. I am probably a little out of touch with this now. I didn't go to either Oxford or Cambridge but they are still regarded as being the best, and rightly so. The teaching at those two institutions is unparalleled. A degree from either of those will be regarded extremely highly by employers. On the next rung down are, I guess, the london Unis and the more traditional redbricks. Outside that, you're going to struggle to get a TC at the top firms. At the very least you'll need some pretty interesting stuff on the CV to stop the application going straight in the bin. Anything other than a 2:1 and you're history but you know that.
Cottonmouth asked about what books to read - don't worry yourself about that at this stage. I would, however, recommend that you start getting to grips with the business press. If you intend being a commercial or "City" lawyer then you will need to understand how the business world works. Start to read the decent broadsheets (and that means the business pages not just the sport!).
As for working overseas, that very much depends on your area of speciality. You are likely to be limited to working in those jurisdictions which have a similar legal system and laws to England & Wales - Australia is the best example. A few years post qual experience is normal. English lawyers are well thought of overseas - generally we benefit from good teaching, good training and the legal work in the City is arguably the best in the world. To answer someone's question - experience in Scots law will not be as well regarded as English law experience as the systems and laws are markedly different. Its not impossible, but it will be difficult.
Finally, someone asked about how much we get paid. I've seen some hilarious stuff posted on this site about how much solicitors and barristers earn, especially about the latter. The rollonfriday website has some good info about payscales for the main firms. Lets just say we don't go hungry.
Hope that helps.
Keep the questions coming - please note, however, that the time difference means that my answers are always going to be a bit late. The more specific the question the better.
Chalks.