Enjambment in poetry is where, as Wikipedia puts it, "the meaning 'runs over' or 'steps over' from one poetic line to the next". Here's an example from Big Thief's Simulation Swarm:
Once again, empty horses
Gallop through the violet door.
The opposite of enjambment is end-stopping. In the following excerpt from Bob Dylan's I Want You, line 3 is enjambed, while the rest are end-stopped (more analysis here):
The guilty undertaker sighs
The lonesome organ grinder cries
The silver saxophones say I
Should refuse you.
In some cases, like the examples I just gave, enjambment and end-stopping are very obvious. But sometimes, it's not so clear. If I had to pinpoint the moment when I first learned to appreciate modern poetry, it was when, aged 14 or so, I encountered these lines from T.S. Eliot's The Love Song of J. Alfred Prufrock:
In the room the women come and go
Talking of Michelangelo.
The meaning does indeed 'run over' from line 1 to 2, but at the same time, line 1 is an independent finite clause (i.e. it can stand on its own as a sentence). So I'm not quite sure if it's technically enjambed, end-stopped, or a secret third thing. I haven't looked into this in depth, but I suppose the answer might also depend on how exactly you define enjambment. According to this typology, I think the Eliot couplet is an example of cross-clause enjambment.
Then there are broken rhymes, where a line break occurs in the middle of a word, as in Willard Espy's The Unrhymable Word: Orange:
The four eng-
ineers
Wore orange
brassieres.
And just when I thought this could go no further, I found the delightful Essay on Enjambment by Raymond Griffith, where a line break splits a single letter (W) into two Vs.
When texting, if you press send in the middle of a sentence, it's a sort of line break. Some of my friends write longer, sometimes paragraph-length texts, while others break up their missive into shorter fragments. My friend Violet is an extreme example of the latter, and lately I was thinking how many of her texts read like skilfully enjambed poetry.
Another example:
wanted to share the joy that
i got a violin!
...and a longer one (all texts quoted with permission):
i was trying to look for lye
to make cold pressed soap
singapore is really
so regulated