Areal Density - Generally measured in bytes/sq. inch. The higher this number is, the more bits will fall under the hard drives read heads per second, resulting in higher transfer rates. Areal density is often overlooked when hard drive shopping, but the truth is that this can have as much of an impact on the drive's performance as the rotational speed. Higher areal densities mean bigger hard drives and faster transfer times.
Rotational Speed - Generally measured in Revolutions per minute (RPM), and most current drives range between 4,500RPM to 12,000RPM. Rotational speed directly correlates to the performance of the drive. Doubling the rotational speed effectively doubles the rate at which data can be stored or retrieved if everything else is held constant. Usually a higher rotational speed means better performance, and is one of the first things to look for when shopping for drives.
Seek time - Time it takes to "find" a track on a disk. This number is often used in a very confusing manner. Sometimes a company will list a track to track seek time (which is a best case number between 1-4ms) or an average seek time (which is usually between 6-13ms). This number will likely not affect your buying decision as all drives in the same price range are usually within a millisecond of each other.
MTBF - Mean Time Between Failure. This is the duration of on time that the drive is meant to continue working. Most of these times are far longer than you would want to keep the drive anyway. This number should generally be ignored.
Cache - The place where data is buffered between the platter and it's final destination. A big cache usually means big performance, but there comes a point where adding more will do nothing for you except raise the cost. Don't pay more for a bigger cache if the performance gains are only marginal. Other factors such as rotational speed and areal density play a bigger role in the performance of a hard drive.
Platter - The disk itself. The platter is coated in the magnetic material that stores the 0's and 1's. Most hard drives have multiple platters. Most platters are 3.5 inches in diameter, and should not vary in any way that would affect your buying decisions.