Malted grains are the basis of all-grain brewing. They are the kernels, or seeds, of cereal grains (usually barley) that are allowed to germinate and sprout before being heated to stop the growing process. This heat also converts some of the grains' starches to sugar and changes their flavor profile.
How the grains are heated makes a huge difference in the kind of malt they will produce. A certain variety, the crystal or caramel malts, are heated in water in a way that converts most of the starches to sugar inside the kernel, resulting in a malt that does not need to be mashed.
At the other end of this spectrum are the kilned malts, or malts that are heated at a relatively low temperature to get rid of most of the moisture from the germinating process. How the grain is treated during and after the drying process makes for a huge amount of variety in the resulting malts.
Kilned and roasted malts are grains that are first dried at a lower temperature, then roasted at a higher temperature. This makes for strong, dark, toasty flavors that can do a lot for a beer's ultimate taste.
Unfortunately this roasting process (and this goes for the crystal malts, too) does away with a lot of the malt's diastatic power. Diastatic power is a grain's ability to convert starches into fermentable sugars. The roasting process gets you part of the way in this conversion, but it's mashing that does the bulk of the work, and mashing is dependent upon the presence of diastatic enzymes.
Diastatic enzymes, unfortunately, can't survive the high heat necessary for most roasting and even some kilning processes. That's where base malts come in.
Base malts are, to put it simply, the least messed with of the malts. Barley kernels are allowed to germinate, then they are kilned at a temperature just high enough to dry out the moisture.
The low heat means that pretty much all of the diastatic enzymes survive, and the resulting malt has lots of diastatic power.
You need diastatic power to make a mash work. Otherwise, you'll wind up with beer that doesn't ferment all the way and has a very low alcohol content. Base malts get their name because they are almost always the base of the beer, the majority of the grain bill that ensures that the beer ferments completely.
While a roasted malt may not be able to convert its own starches to sugar, the presence of lots of base malt ensures that it does. Base malts basically convert their own starches and, in the process, pick up any starches nearby and carry them along for the ride.
There is something of a trade off for all that diastatic power. Since they're only lightly kilned, base malts lack the intense malty, toasty, and chocolaty flavors present in other malts. They're far from flavorless, of course, but they're less defined. Considering the fact that they're used in such high quantity (often as much as 10 lbs per 5 gallon batch), this subtlety of flavor isn't such a bad thing.
And considering that bulk, the subtle aspects they do have are usually able to shine through.
Though subtle, base malts do come in different varieties that have their own distinct qualities. Here are a few main ones:
Pale Malt - This is by far the most common base malt, sold in both two-row and six-row varieties. It can be used as a base for both lagers and ales.
Pilsen Malt - This is used traditionally to make Pilsner beer and is useful for many German and Belgian style recipes. It is kilned at a slightly lower temperature than pale malt, and has a crisper and less toasty flavor.
Pale Ale Malt - This is very similar to the pale malt, but it's kilned at a slightly higher temperature. This makes for a stronger malt flavor and a darker color. It tends to be used only for brewing ales.