A Bitcoin ATM is a machine that buys or sells bitcoins for cash.
It works almost like the ATMs you use today.
There are a few differences:
Instead of inserting your debit card and getting cash, you insert cash and get bitcoins sent to your Bitcoin wallet (if you are buying bitcoins).
Some Bitcoin ATMs also let you sell bitcoins, so you would send bitcoins to the machine and the Bitcoin ATMs would spit out cash.
Bitcoin ATMs are a good way to buy bitcoins if you have one near you. You can use Coin ATM Radar's map to find locations.
Delivery of bitcoins with Bitcoin ATMs is instant, so you get your coins fast.
Buying bitcoins with ATMs is also private, since no personal information is required at most ATMs.
The average fees are about 5-10%, although this can vary greatly depending on your country.