In Parhsat Tzav, Vayikra 7:24, we read:

The fat of a neveilah (an animal that died) and the fat of a treifah (an animal that had been torn to death) may be put to any use; but you shall not eat it.

A neveilah is a kosher species of animal that died without shechitah (ritual slaughter) and is therefore not kosher.

A treifah is an animal that was mortally wounded and then killed by shechitah or an animal that had a disease or a wound in a vital organ that would cause it to die within twelve months. In these cases, shechitah doesn’t help and the meat would be forbidden.

The Talmud, Chullin 42a (the first Mishna in Chapter 3) lists 18 different defects that render an animal a treifah.

The Gemara explains that we learn about treifah in Parshat Mishpatim, Shmot 22:30:

You shall be people of holiness to Me. You must not eat treifah (flesh that was torn off) in the field. Throw it to the dog.

Rashi comments:

If you will be holy and abstain from the abhorrence of eating neveilah and treifah then you are Mine. But if not, then you are not Mine.

Yaakov uses the word treif in the Book of Breisheet:

In Breisheet 37:33, when Yaakov is shown Yosef’s blood stained coat he says:

“My son’s tunic! A savage beast devoured him! Tarof Toraf Yosef (he has surely been torn to bits).”

When Yaakov gave Binyamin his blessing, in Breisheet 49:27 he said:

Binyamin Ze’ev Yitarf (is a predatory wolf). In the morning he will devour prey and in the evening he will distribute spoils.

We see from here that although people use the word treif to mean non-kosher, that is not really the case. The prohibition against eating non-kosher animals and meat and milk together has nothing to do with the word treif which refers specifically to flesh that was torn.