Witnesses keep the steemit system running

they are like Miners for the Steemit-Blockchain

you can more or less look at the Posts, upvotes, etc. as an equivalent to the Transactions in Crypto Currencies.
Blocks of these actions are then verified and chained together - so you have the Blockchain.

The Witnesses therefore have to bring up a Server, powerful enough to keep everything running.

Other important traits would be

• Location (a distributed chain is less vulnerable to attackers)
• Reliability (a secure Appearance as well as the technical connection)
• Speed (again the Internet connection)
• Mining Power (As said: a powerful rig)

These things are mostly the content of the Witness applications.

you can also find a little bit more about it here or here.