Short of an actual dentist, I am unfortunately pretty close (so no official medical advice here - I'm not that kind of doctor) to an expert on the subject, having had about 12 root canals and about 2 or 3 retreats - genetic, I expect, it's not like I haven't brushed and flossed twice a day my whole life - my dad has had root canals on all his teeth (although he now only has about 10 real teeth left - the rest is all bridges and plates).
The reason for the root canal is that the infection often doesn't just go away by itself or even with antibiotics (you will often notice an improvement after antibiotics, but that is just because the infection that had spread to surrounding tissue is healed). I don't know the exact reason for this, but I expect that it is because the pulp of the tooth doesn't have very much in the way of blood flow - especially when an infection is present. This means that the bacteria is still present and can re-infect the surrounding tissue again a few weeks or months later.
During the actual procedure they core the nerve and some of the pulp out. SA and UK dentists apparently only remove the central bit, whereas US dentists try to remove all of it, in order to reduce the chance of further infection, requiring a re-treat. I've never needed a re-treat on a US root canal (had about 5 here, and two re-treats of the SA root canals). By removing the nerve pulp, the bits of the infection that your body could clean up by itself are removed. By sealing up the root canals, it prevents a further chance of reinfection - this doesn't always work (it does work 90% of the time or so in my experience), and then if possible you can attempt a re-treat. If this fails, you will likely have to have the tooth removed.
The root canal procedure isn't that bad actually. It's not a coin flip, the probability of success really is pretty high. I strongly recommend keeping the tooth - having a tooth out sucks, it's risky (I had it done a few times, and once they cracked the adjacent tooth in the process). It's prone to infections, and also a wonderful condition known as dry socket, when your clot falls out. Also, over years of having a gap, your teeth could start to wander, creating more gaps between your other teeth, which could be visible, but even if not, could be a hazard in terms of decay and cavities. Just leaving a gap also means that impact gets redistributed onto fewer teeth, the opposing tooth doesn't have anything to press against, etc. Essentially all mechanical problems that can lead to further complications with your teeth.
Also, getting a fake tooth put in is crazy complicated. A bridge generally requires a root canal on at least one adjacent tooth to support it via a crown that goes over both (or all three). An implant (I've had two of these f**ckers) is an unbelievably crazy process, requiring extraction, bone grafts, drills (not the "wee-wee" sounding ones - something that looks like the one your dad used to install the new front door), hammers, titanium screws, etc.
I suggest getting the root canal, getting a filling if enough tooth is left, otherwise a crown. This will likely serve you fine for 10-20 years before you need more work done (and there will likely be better technology then anyway). Be sure to ask for an antibiotic right after the procedure.
Good luck.