An intersection is a place where two or more roads cross each other.
When we talk about intersecting things, it usually means they meet at one point. Imagine being on your way to school and turning left onto Main Street - as you drive down that street, you'll intersect with several other roads. You might also think of two lines intersecting on a graph or map: the lines don't touch anywhere else, but they definitely cross paths at this specific spot. Sometimes we use "intersect" for events too: if two friends are in different parts of town and meet up at a café, you could say their schedules intersected.
(ambitransitive) To cut into or between; to cut or cross mutually; to divide into parts.
Example: Parallel lines don't intersect.
