What is the meaning of the word "border"?

Definitions:

a strip forming the outer edge of something noun
- the rug had a wide blue border
to enclose in or as if in a frame verb
- We bordered the painting and it cost us a lot.
to extend on all sides of simultaneously verb
- The forest bordered the lake.
to form the boundary of verb
- The river borders the west side of our town.
to lie adjacent to another or share a boundary verb
- Pennsylvania borders Ohio.
to provide with a border or edge verb
- They bordered the painting with a white mat.