A bit of easy expansion
500GB in an external hard drive would be a decent amount of storage for a backup drive or even to extend your laptops space for a cheaper amount as getting a laptop with more space definitely costs more. Storage space is important today as people end up saving so many different files from work to music to pictures & videos.
Backing up your files
The advantage of a regularly backed-up drive cannot be overstated, one may not be as sad about their laptop dying as they would be about losing their files. Aside from that being compact is a plus to store or carry around as most drives fit in the palm of your hand so it wouldn't take up much space in a drawer or safe.
Most connect through a USB or FireWire but there are also drives that use eSATA and Wifi. External Hard Drives that are larger usually require an external power source as well. But with a 500GB one you should be fine using just the connector port. Unless it is a WiFi-based connection, then the drive would need electricity to power up its Wifi system.
Internal build variation
External Hard Drives also have 2 different types of builds, the Solid State Drive (SSD) or the older HDD. The SSD is more robust over time as it has no moving parts and uses electronic circuits to write and retrieve information which also makes it faster than the HDD. There are also options to buy one with a rubber coating for rugged use.
Available in many brands with the more known ones being Western Digital, CalDigit, Seagate, LaCie, ADATA and Samsung among others.