They are little levers that are used for getting tyres off a wheel. A set of levers are one of the cheapest and most essential bits of cycling equipment. Everyone should carry them. Many tyres are almost impossible to get off without a set of levers. If you ever get a puncture you could be properly stuck if you don’t have some tyre levers handy.
There are lots of different designs of tyre levers but they all basically have the same function. A thin end used to slide between the tyre and the rim of your wheel to get the tyre off. If you have relatively loose-fitting tyres then this may be enough. On Tighter tyres you may need to use a second lever a bit further along the tyre. Levers normally come in sets of three but you should only need the third lever on the very tightest tyres. The other end of the lever will normally have a little hook on it. This is to hook onto a spoke to hold the lever in place while you put the second one in.
Traditionally levers would be made of steel or aluminium, These days most people use plastic levers. These are not only lighter and easier to carry. They are less likely to damage the rims on your wheels or the bead on your tyre.
Tyre levers should normally only be used to get your tyre off, not to put it back on. If you do this it's really easy to get the inner tube trapped between the tyre and rim. If this happens you'll hear a deafening bang as your inner tube explodes when pumping the tyre back up. Not something you want to happen, especially if you are miles from home.
This video from Park Tools takes you through the whole process of fixing a puncture. Including the proper use of tyre levers.