The word milchig refers to dairy food as it pertains to mixing meat and milk, a prohibition we learn from the Torah commandment not to cook a calf in its mother’s milk.
There’s a funny joke on the topic.
Hashem says to Moses “Don’t cook a calf in its mother’s milk.”
Moses replies: “Oh so we need two dishwashers, one for meat and one for milk.”
G-d: “No; just don’t cook it in the milk!”
“Oh, so we need to wait six hours in between meat and milk?”
“No; just don’t cook it in the milk!”
“So, we need to wait three hours?”
G-d: “No; just don’t cook it in… You know what? Do whatever you want!”
Another unique thing about milchig is that there is an ancient custom to eat milchig food on the upcoming holiday of Shavuot, the holiday on which we celebrate our receiving the Torah. As a carnivore myself, can’t say I love this custom.