In the torah there are lots of laws about animals like which ones you can and can't eat and which ones are allowed to plow your fields. If you're plowing a field and you have an ox and a goat pulling the plow you would be breaking one of the many laws of torah. You must have animals of the exact same strength, so one doesn't overpower the other and maybe hurt the weaker one. I learned that the Talmud forbids eating meat and milk together. The Talmud wants you to think about the fact that the meat you are eating was once a living animal.
Milk represents life and meat represents death.
When you separate meat and milk you are separating life from death. May every living creature thank you and praise you faithfully, throughout the Universe. You also say this prayer for a special occasion. However you don't say this prayer when you put on something made out of leather. The enjoyment of having those new shoes or jacket is lessened because it cost an animals life.