We use these to manipulate DNA to splice into bacteria in labs, by putting artificial restriction sites on the DNA to be inserted and identifying a part of– usually — a plasmid, which is a free floating strand of genetic material outside the main bacterial genome that allows the bacteria to do extra stuff (a lot of antibiotic resistance is carried on specific plasmids and can even be acquired by living bacteria that integrate DNA from dead ones.)
Restriction enzymes make “L” shaped asymmetric cuts, so if you have two pieces of genetic material cut with one enzyme, the two can interchangeably dimerize with each other.