What does it mean to cure meat?

To dry it out, flavor and preserve the meat by means of salt and (usually) spices.

It breaks down the meat , corned beef is brined or cured.

Why is corned beef is pink after cooking.

It’s just a primitive form of storing meat so it stays good to eat longer, minus refrigeration usually.

Meat is cured to make it last longer. Curing meat can be done in a variety of ways. USUALLY it relies heavily on the use of salt. Salt either as a dry rub or in a water solution is antiseptic. When you put salt on or around (as in a solution) a piece of meat, the salt wants to draw out the moisture from the cells of the meat AND the harmful bacteria through osmosis. When enough moisture is removed from the cell of a bacteria, it can no longer survive. Usually somewhere around 3% salt is enough to kill Salmonella. 12% or so is needed for Listeria and upwards of 20% is needed to kill Staphylococcus.
Often spices or even sugar are added to the salt solution to add a new flavor to the meat as it dries.

A brisket of beef is injected with corns (like small gravel) of rock salt to produce a somewhat dry hunk of meat, “corned” beef, that will last some time without refrigeration.
Ham is smoked at a low temperature, cooking it and drying it so that it, too, will last a certain amount of time without refrigeration.
Beef jerky is dried, salted, peppered, and will last a long time until eaten, or prepared with water, potatoes, tomatoes, etc., as stew or soup. Fish can be cured the same way.
And salt pork.

Spank that naughty ole meat, that’ll cure it!! >8^O

I’ll go look that up for you right now.