Both Uses of

arbor

in

Much Ado About Nothing

I will hide me in the arbour.†
Scene 2.3 *

unconventional spelling: This is a British spelling. Americans use arbor.

Definitions:

(1) (arbor as in: shaded arbor)
a framework that supports climbing plants; or a shady rest area made by such a framework or by trees and shrubs

The framework of an arbor is generally thought of as a wood lattice made to support vines, but it can also be a natural framework such as trees.
(2) (meaning too rare to warrant focus)
Much more rarely, an arbor can be used as a proper noun to reference a location. As a common noun, it can also reference various types of rotating machine shafts.