12-Cup Brewing is the traditional style of drip coffee brewer, where you add ground coffee in a filter and wait for hot water to drip through to eventually make a pot of fresh coffee. Of course, this style doesn't only come in 12 cup sizes. You can get drip coffee machines in 10, 8, 4 or even 1 cup capacities if you don't use as much coffee every day. These are the coffee-makers most people are familiar with, which is their biggest positive feature. Everyone knows how to use them, and they all use the same kind of ground coffee without having to get anything special. Your choices for makes and models are almost endless, ranging from cheap department store machines to high-end and gourmet equipment. But you do have to measure out the loose coffee grounds, and deal with filters full of wet grounds after each pot of coffee. It's not a particularly large task, but it can get tedious after a while.
The biggest drawback of the drip coffee maker is the time it takes to brew. Most large machines have some kind of a "pause n' pour" valve that allows you to take the pot out of the machine and pour a cup before the entire brewing cycle is done. Even so, waiting for coffee to brew, drip by drip, can be painful. Single Cup Brewing This is the newer kind of coffee machine, that is designed to brew one cup at a time rather than a complete pot. The trick is that the water is slightly pressurized to speed up the drip-by-drip process. So a cup of coffee can be made in a matter of seconds. Every cup is fresh and fast. In this case, the negative is that you have to use the right kind of "pods" for the machine. They don't take loose coffee grounds.
Some machines, like the Senseo, the One:One and the My Cafe all accept the same type of simple pods that look like a teabag filled with coffee grounds. They are easy to find because many machines use them, and you can get a whole line of coffee varieties and even some teas in pods. More complicated machines like the Tassimo or the Keurig only accept their own type of pods (called T-discs and K-cups respectively). They both have very diverse lines of coffee, tea and hot chocolate that you can choose from but you are limited to the one type of pod only. The generic "Senseo-style" pods are more expensive than loose ground coffee, but not that costly. The specialized pods for Tassimo or Keurig are more expensive again.
So when you are trying to decide between single cup or 12-cup brewing systems, you are basically choosing between a slow but inexpensive option versus a quick and expensive one. Do a little research and see which will suit you best.