Halal just means "acceptable" the opposite of Haram which means "prohibited", for some Muslims things such as pork, alcohol, etc. are prohibited, whereas beef, lamb, chicken are Halal/accepted only if the slaughter is performed in a specific manner under the observation of a qualified Muslim. As mentioned above, Halal slaughter requires the animal be facing a certain direction, that a fatal cut be made to the throat, and that a prayer is spoken during the slaughter (there is some controversy on this last point, some larger chicken processors just play a recording, some Muslims don't like that). In the beef and lamb plants that I've been in doing a Halal slaughter, the animal is first stunned, either with a bolt or an electrical stun, and then the throat is cut and it is bled out. The only difference between the Halal slaughter and the normal slaughter, is that a Muslim is holding the knife.
There are also some stipulations about how the meat is handled post-slaughter, mostly regarding the separation of Halal meat from non-Halal. Real sticklers will want it stored in separate coolers, but most Muslims eating Halal in my experience are fine as long as proper measures are taken to ensure that no cross contamination occurs.
Halal certification gets a bit trickier. To ensure that meat is Halal, you need to pay someone to certify that your processes were proper. Many Halal certification organizations will insist that the original Halal certificate has to accompany the meat throughout the distribution chain, this gets pretty tricky when loads get broken out. So technically, if you've got something with a Halal mark on the label, but you don't have the cert, it's not Halal anymore, but there is a lot of wiggle room. Part of being a good Muslim eating Halal requires them to get to know their butcher so that they can trust what he is selling them. We sell all kinds of Halal items without certification or documentation at all, and we put a Halal mark on our further processed items that use all Halal ingredients, we've never had any problem because we try and be very transparent about this on our website so our customers know exactly what they are getting. Halal does not have nearly as much central control or recognition as Kosher so there is a really broad range of categories that pass as Halal and some specialty retailers even go so far as to rank their products in terms of Halal-ness. Also, certification authorities like to say that competing certification authorities are not "real" Halal, but that tends to happen when money is involved.
Halal has nothing to do with quality, just like anything else, there are some Halal products that far exceed commodity level, and some that are far below it. You've probably eaten Halal products many times without knowing it. Pretty much all chicken from Brazil, lamb from Australia, and Lamb and Beef from New Zealand are Halal. Also, many plants in the US slaughter everything Halal, and then just pay for certificates on the product they export to Islamic countries.
I have occasionally run into prejudiced individuals who don't want Halal product, but like most prejudice, they are really just ignorant, and occasionally stupid...
Most Muslims, by the way, consider Kosher to be acceptable as Halal. But it doesn't work in the other direction.
I'm not Muslim so I could be wrong about some of the above, but I do have loads of Muslim friends and we sell a fair bit of Halal product and so this is what my understanding is up to this point.