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$$m$$ and $$n$$ are any two non-parallel lines and $$l$$ is another line intersecting them at $$A$$ and $$B$$.

Such intersecting line ($$l$$) is called as transversal line.

A transversal line is a line that intersects  two lines at distinct points.

The line $$l$$ is not a transversal to the lines $$m$$ and $$n$$, but it is a transversal to the pair of lines $$m$$ and $$o$$, $$n$$ and $$o$$.

Line $$l$$ does not intersect the lines $$m$$ and $$n$$ at distinct points. So, it is not a transversal line.