The old hard disks feature one or more rotating rigid platters on a motor-driven spindle within a protective enclosure. Data is encoded magnetically by read/write heads that float on a cushion of air above the platters. It is noisy and quite big in size.
Now the new type of hard disks are called flash-based Solid-state Drive (SSD) use microchips where data is retained in non-volatile memory chips and contain no moving parts.
Comparing both of them together,
Here is a link that compares both of them side by side.
The use of flash-based SSD was one of the main reason why it is possible for the MacBook Air to look like this:
