Besides being the name of an opera, aida is also a very popular fabric for cross-stitching. Aida is characterized by being:
Coarse means that the threads are thick and there are relatively few of them. Stiff means that the material doesn't bend and curl easily, so it's easy to handle one-handed while stitching. Even-weave means that it has the same number of threads per inch both up-down and left-right. But the open-weaving is what makes aida specially suited for cross-stitching.
Open-weave fabric is any fabric that is woven to have holes in it, rather than being solid and smooth. Cheesecloth is basically the open-weave concept taken to its logical extreme. Aida doesn't quite go that far, but it has holes set at even intervals. These characteristic holes are what makes aida good for cross-stitching, they provide natural places to stitch through so the crosses come out square and even. Because of these holes, cross-stitching can be done with a thick, blunt embroidery needle that is easy to thread, since it doesn't need to be sharp or thin to pierce and pass through the fabric.
Aida comes in several different sizes, defined by how many holes per inch are in the cloth. For example, the most popular size, 14-count aida, has 14 holes per linear inch, measured both up and across because it's even-weave. A smaller number, such as 10, means fewer holes per inch, so the stitched crosses will be larger. Conversely, a larger number, such as 18, means more holes per inch, so the crosses will be smaller. This directly affects the size of the final design and can be thought of as the resolution of the fabric.
The stitching between the holes also has a characteristic appearance, which makes it easy to count holes when placing stitches. The weave consists of woven groups of threads, so all the threads between two holes will be aligned in the same direction, like this:
||| ≡ ||| ≡
≡ ||| ≡ |||
||| ≡ ||| ≡
The corners of the groupings are where the holes will be found. A cross-stitch is made by starting from one corner, stitching over to the diagonally-opposed corner, then stitching across the backside to an adjacent corner, then stitching over the front to the remaining corner, creating an X. While the stitching will go through the holes for cross-stitches or half-stitches (a slash / rather than an X), there is also a technique called quarter-stitch, which requires the needle to penetrate the fabric at the middle-center of the thread group between the holes. The result is one-quarter of a cross. This uncommon technique is used to create a different effect in the stitching that can increase the perceived resolution of the pattern or transition colors.
The higher the count, the fewer plies of floss will be used to make the cross-stitches. The lower the count, the more threads will be required. This is because more plies means thicker stitching, which is needed to fill the extra space of lower-count aida. 10-12-count needs 3 or 4 plies of floss. 14-count needs 2 or 3 plies. 16-18-count needs 2 plies. 20-count or higher will only need 1 ply. Of course these are only recommendations, and using more or fewer plies can achieve different effects.
Because aida is stiff, it doesn't necessarily require an embroidery hoop to hold the fabric while stitching. Some people like just letting the stiffness of the fabric hold itself out while stitching. An embroidery hoop can, of course, be used if desired, but keep in mind that the stiffness also means that it will hold the crease the hoop creates after it is removed. The fabric can be ironed to remove these creases when the project is finished.
Aida comes in a variety of colors, the easiest to find being white, followed by black in a distant second. The color of the aida will often function as the background to the design, or else the entire background will need to be filled in with tedious stitching in the appropriate color (which does look better, though). The widest variety of colors can be found in the popular 14-count size, it can be very difficult to find anything other than white in other sizes.