Bitcoins sent to these addresses are gone forever. There are a few reasons whey people might send to a burn address. Primarily, sending to a burn address proves that you spent the bitcoins and got nothing in return. Some people send just like some people might burn a $100 for show in a video. Many of the bitcoins sent to 1111...4oLvT2 were sent accidentally due to software bugs.
It is called a "burn address" because bitcoins sent to it can never be recovered. They have been "burned".
A burn address is an address with an unknown private key. It is not possible to prove that the private key for a burn address is not know, but we can be pretty certain that the private keys for these addresses are not known because addresses that have private keys must be mostly random and those addresses are far from random.
Burn addresses are easy to construct. In short, you set all but the last 6 characters in the address to the text that you want and then compute the last 6 characters as the checksum.
Burn addresses such at those cannot be made with a vanity address generator.