|A smiley-face penny|
The face was probably cut out of the penny using a process called die cutting - a die (a shaped blade or punch) is pressed by a machine into some material (in this case, the zinc of a modern penny) to cut it into a shape (in this case, to cut out 2 eyes and a mouth). A plain round hole can be made in a coin using a drill, but shaped holes like these would be difficult to do, and to do consistently.
Coins like these are frequently sold in souvenir or gift shops as "Lucky Pennies" - to buy as a gift for someone so that they will have good luck while they are carrying the coin. This is a variation on the rhyme "see a penny, pick it up, all the day you'll have good luck" - the idea that finding a penny is considered good luck. The face certainly makes the penny look more interesting than one that you might find on the ground, but I'm not aware of any studies to determine which type of penny will bring you more luck.
In my previous post about world coins with holes, I mentioned that coins with holes drilled into them are worthless as collectibles. While a shaped hole like this makes the coin not valuable to a coin collector, there are people who specifically collect coins that have been die-cut in this manner (similar to how other collectors seek elongated or "smashed" pennies). Anyone with a drill can cut a round hole in a coin - they are not hard to make, so it would be very unusual to find someone interested in collecting coins with drilled holes. But die-cut coins require expensive tools; they are more rare and so some people do collect them.
Because pennies are considered mostly valueless in the United States (many simply get thrown away every year), you would probably find that most stores or banks would take an occasional penny like this as payment, and then simply throw it away (or keep it as a novelty item). But "Lucky Pennies" usually cost much more than $0.01 to buy at a gift shop, so there is not much value in buying them and then trying to use them as money.
Cutting holes in a United States coin like this may technically be illegal under US law (US Code Title 18, Section 331). But in practice, the law is usually enforced only when coins are changed for fraudulent use - such as cutting a penny down to the size of a dime (to use in vending machines), or painting a quarter gold so that can be passed off as a US dollar coin.
Even though it's not really what I collect, I'm going to keep this little guy because it makes me smile.