Even though we never directly see the garden of Sidley Park, its symbolic presence is felt throughout the play. Hannah, especially, has Opinions about what the history of the garden means:
BERNARD: Lovely. The real England.
HANNAH: You can stop being silly now, Bernard. English landscape was invented by gardeners imitating foreign painters who were evoking classical authors. The whole thing was brought home in the luggage from the grand tour. Here, look – Capability Brown doing Claude, who was doing Virgil. Arcadia! And here, superimposed by Richard Noakes, untamed nature in the style of Salvator Rosa. It's the Gothic novel expressed in landscape. Everything but vampires. (1.2)
Hannah's main objection to the landscape is its triteness: it pretends to be natural, but really it's just riffing off of imaginary landscapes from the past or from literature (or from past literature). The so-called "real England" is actually a mash-up of French and Italian fantasies of what Ancient Greece was like.
The idea of coming up with an ideal natural landscape in order to make up stories about nonexistent past is a long tradition that usually goes by the name "pastoral." Pastoral art and literature imagines a green countryside populated by shepherds, shepherdesses, and very well-behaved sheep who pretty much take care of themselves so the shepherds and shepherdesses can spend all their time flirting with each other. The pastoral portrays a rural life where people survive just fine without doing any work – which, as anyone who's ever lived on a farm can tell you, is totally unrealistic.
The pastoral-life-magically-without-labor transforms into a landscape-magically-without-labor: Bernard calls it "the real England," as if it's what England would look like if no one did anything to it, when really it's the product of a bunch of gardeners and landscape architects working very hard to create the illusion that they didn't do anything at all (kind of like well-applied makeup).
Alongside the pastoral, we also get the picturesque, which is also a style of landscape that pretends to be natural while actually being totally made up. But the idea of nature behind the picturesque is very different. While the pastoral takes a Disneyland version of ancient Greece as its inspiration – green rolling hills and nicely-spaced trees – the picturesque takes a darker approach, with rugged crags and mossy ruins (all trucked in by order).
So what does this all mean for the garden as a symbol in Arcadia? One implication is that the landscape's changeability questions the very idea of the "natural" – what seems natural at first glance turns out to have been very carefully designed to create that effect. And this whole idea of erasing labor also connects to genius, the person who is struck by inspiration rather than having to work for it. If the labor-free landscape is an illusion, could genius work the same way?
(See also "Classicism vs. Romanticism" below.)