In the article How Hard Disks Work, you can see that the read/write heads are touching the platters in the drive. When the platters spin up, they rotate at anywhere between 3,600 rpm and 7,200 rpm.
To the head, the platter seems to be moving at about 150 mph, and a very thin cushion of air forms between the head and the platter so that the head "flies" over the platter. If even the smallest bit of dust makes its way onto the platter, the flight is disrupted and the head "crashes" into the platter, scratching it. The crash, of course, sprays a lot more dust and debris onto the platter and then it's all over.
The other thing that can cause a squealing sound is the bearings in the drive motor. That is another common way for a drive to fail.
Hard disks are amazingly reliable these days, with "Mean Time Between Failures" (MTBF) of 500,000 to 1,000,000 hours. That means that, on average, a drive fails after the specified number of hours, with half of the drives lasting more than that and half lasting less. 500,000 hours is about 57 years. Clearly, not all drives last 57 years, so frequent backups are important.
Here are some interesting links: