A run-on line is a poetic line that carries into the next line without a full pause or a completed thought at the line break. The sentence or phrase keeps moving, so the reader has to continue to the next line to finish the sense. This is often called enjambment.
Example
The rain keeps whispering at the window
while the streetlights tremble in the dark,
and morning waits just out of reach.
Related Definitions
[adj] (verse) without a rhetorical pause between lines
[v] talk or narrate at length
[v] continue uninterrupted; "The disease will run on unchecked"; "The party kept going until 4 A.M."