The idea is: if web-surfer visits several of your pages (staying several seconds on each) – he/she gets the reward in form of the juicy faucet. To encourage the visitor the countdown visualization is presented.

See in action (look for the coin with the countdown in the right top corner) :
https://wmexp.com/remotely-hosted-bitcoin-faucet-examples-list/example-surfer-reward/

Source code (GitHub): https://github.com/gra4/Satoshi-Visitor-Rewarder

Also available in WP Plugin: https://wordpress.org/plugins/simple-bitcoin-faucets/