To be beside oneself with uncontrollable anger; enraged.

Example: People can get upset, and some might become so infuriated that they yell or even throw things. Well, one might describe the person who is acting in such a way with the idiom 'foaming at the mouth.'
This phrase likely originates from viruses, such as rabies, that can cause literal foaming at the mouth. Rabies is a deadly virus that both humans and animals can catch. A bite from an infected animal, like a bat, is usually how this virus spreads. One symptom of rabies is that it makes swallowing very difficult. Consequently, saliva builds up and there is a "foaming" at the mouth.

This idiom is at least over 400 years old. For instance, in 1601, William Shakespeare, a famous poet and playwrite, used this common expression in the play Julius Caesar:

    "He fell down in the market-place, and foamed at mouth, and was speechless."
Common Phrase Origins and Meanings  |  F-Letter Expressions
Note: There are times when a phrase's origin is unclear. If that happens, what is usually provided on a page are the popular or plausible theories that are around that talk about how a phrase may have originated. If not that, then I'll typically try to find the earliest quote that I can of an expression being used in writing. These generally come from old newspapers, books, or poems.

The quotes are meant to give you an idea on how far back in history the expression goes. So, for example, if I quote a book from 1600 because it uses a certain idiom, then it's at least that old.

* That dude is so angry, just look at him; he's foaming at the mouth and throwing things around, we should probably leave before he catches sight of us.
Phrase Meaning for Fight Fire With Fire.
Origins for the saying Foaming at the Mouth. - Meanings and Origins of Phrases 
A list of phrases starting with the letter - F.
Phrases and Idioms