What do restriction enzymes look for in DNA?

Palindromic sequences - short stretches that read the same on both strands in the same direction, like GAATTC paired with CTTAAG. A restriction enzyme recognises one specific sequence and cuts there, every time, which makes it a molecular scalpel with a fixed address.

They exist as a bacterial immune system. Bacteria are attacked by viruses, and these enzymes chop up invading viral DNA at recognised sites while the bacterium's own DNA is protected by chemical tags at those same sites. The name is literal: they restrict the growth of a virus.

Discovering them made genetic engineering possible, and that is not an overstatement. Being able to cut DNA at a predictable point and then paste fragments together is the whole basis of recombinant DNA - it is how human insulin came to be produced in bacteria from 1978, replacing insulin extracted from pig and cow pancreases. The work won a Nobel Prize in 1978, and the field it opened is why CRISPR, a different bacterial defence system repurposed the same way, was recognised as important so quickly forty years later.