Wipe, in a computing context, means to render all data on a hard drive unreadable. The term is often used in reference to making data stored on a computer, smartphone or tablet inaccessible before disposing of the device.
Although "erase" is often used as a synonym for "wipe," that term is a little misleading -- it isn't possible to actually erase hard drive data. Deleting a file only removes the file listing, which serves as a shortcut. The data is still on the computer and easily accessible to anyone with the right program and/or know-how. The same is true if you reformat a drive.
The most common method of wiping a computer's data is to use a hard drive overwriter product, such as Darik's Boot and Nuke. The more times data is overwritten, the more unreadable it becomes. The most thorough products overwrite each bit with a zero.
The question of whether overwritten data is still accessible is controversial. According to some security experts -- most notably, Peter Gutmann, author of "Secure Deletion of Data from Magnetic and Solid-State Memory" -- an individual with a great deal of expertise and motivation can still access data after a hard drive has been wiped. Some experts recommend that a hard drive should be physically destroyed to ensure that the data doesn't fall into the wrong hands. On the other hand, a NIST (National Institute of Standards and Technology) publication on the issue states that a single overwrite renders data unreadable.
There are various services and products available to physically destroy hard drives. A hard drive shredder is a mechanical device that physically destroys old hard drives so thoroughly that the data they contain cannot be recovered.