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to change from a liquid to a gaseous state, producing bubbles of gas that rise to the surface of the liquid, agitating it as they rise.
to reach or be brought to the boiling point:
When the water boils, add the meat and cabbage.
to be in an agitated or violent state:
The sea boiled in the storm.
to be deeply stirred or upset.
to contain, or be contained in, a liquid that boils:
The kettle is boiling. The vegetables are boiling.
to cause to boil or to bring to the boiling point:
Boil two cups of water.
to cook (something) in boiling water:
to boil eggs.
to separate (sugar, salt, etc.) from a solution containing it by boiling off the liquid.
the act or an instance of boiling.
the state or condition of boiling:
He brought a kettle of water to a boil.
an area of agitated, swirling, bubbling water, as part of a rapids.
Also called blow. Civil Engineering. an unwanted flow of water and solid matter into an excavation, due to excessive outside water pressure.
boil down,

to reduce the quantity of by boiling off liquid.
to shorten; abridge.
to be simplifiable or summarizable as; lead to the conclusion that; point:
It all boils down to a clear case of murder.

boil over,

to overflow while boiling or as if while boiling; burst forth; erupt.
to be unable to repress anger, excitement, etc.:
Any mention of the incident makes her boil over.

boil off, Textiles.

to degum (silk).
to remove (sizing, wax, impurities, or the like) from a fabric by subjecting it to a hot scouring solution.

Also, boil out.
Contemporary Examples

The Race Card and the Jackson Doctor Marcia Clark February 8, 2010
Ask the Blogger: How About That Election? Megan McArdle November 4, 2012
Yes, You Can Change People Benoit Denizet-Lewis January 9, 2010
Will the Young People Go Home Again? Megan McArdle June 11, 2013
Mike Morhaime, the Wizard Behind Blizzard, Creator of Diablo and World of Warcraft Alex Klein June 2, 2012

Historical Examples

The Bontoc Igorot Albert Ernest Jenks
One Thousand Secrets of Wise and Rich Men Revealed C. A. Bogardus
A Chapter of Adventures G. A. Henty
A Busy Year at the Old Squire’s Charles Asbury Stephens
The Library of Work and Play: Outdoor Work Mary Rogers Miller

verb (adverb)
to reduce or be reduced in quantity and usually altered in consistency by boiling: to boil a liquid down to a thick glue
boil down to

(intransitive) to be the essential element in something
(transitive) to summarize; reduce to essentials

verb
to change or cause to change from a liquid to a vapour so rapidly that bubbles of vapour are formed copiously in the liquid Compare evaporate
to reach or cause to reach boiling point
to cook or be cooked by the process of boiling
(intransitive) to bubble and be agitated like something boiling; seethe: the ocean was boiling
(intransitive) to be extremely angry or indignant (esp in the phrase make one’s blood boil): she was boiling at his dishonesty
(intransitive) to contain a boiling liquid: the pot is boiling
noun
the state or action of boiling (esp in the phrases on the boil, off the boil)
noun
a red painful swelling with a hard pus-filled core caused by bacterial infection of the skin and subcutaneous tissues, esp at a hair follicle Technical name furuncle
v.

I am impatient, and my blood boyls high. [Thomas Otway, “Alcibiades,” 1675]

Related: Boiled; boiling. Boiling point is recorded from 1773.
n.
boil
(boil)
To change from a liquid to a gaseous state by being heated to the boiling point and being provided with sufficient energy. Boiling is an example of a phase transition.

Simplify, summarize, or shorten, as in John finally managed to boil his thesis down to 200 pages.
boil down to. Be reducible to basic elements, be equivalent to. For example, What this issue boils down to is that the council doesn’t want to spend more money. These metaphoric usages allude to reducing and concentrating a substance by boiling off liquid. [ Late 1800s ]

boil down
boil over