It means that they come together and intersect.
Lines of latitude are all parallel to each other, so do not converge. Lines of longitude do converge, at the north and the south poles.
The vertex
All the lines of longitude meet or converge at the North Pole - they meet at the South Pole too!
Because unlike lines of longitude which converge on the poles, lines of latitude are parallel to each other: that is, they never converge.
There is no single characteristic for a place where things meet or converge. I would like to say that the place must be something physical, lines can converge on a page (or a screen), people can converge at a lunch table, rail lines converge in many places. However, that place isn't necessarily physical, you can have a meeting of minds, or ideas that converge in a single mind or in time.
All meridians of longitude converge at the north and south poles.
No, this statement is false. Meridians are lines of longitude that converge at the poles, meaning they touch at the poles. Lines of latitude, however, like the equator, never intersect and are always parallel to each other.
Longitude lines show the number of degrees east and west of the Prime Meridian. They are farthest apart at the equator and converge to a single dot at the north and south poles. Latitude lines show distance north and south from the equator. Because they are parallel to the equator, they never converge. Latitude at 90o north and south can be shown only as a dot, not a line.
Parallel lines Never Converge
The point at which horizon lines receding from an observer seem to converge.
In drawing it is the point at which parallel lines appear to converge.
All longitudes converge at the north and south poles.