The pattern がある + Noun uses a relative clause with がある to modify a noun, describing it as "a noun that has ~" or "a noun with ~." In Japanese, relative clauses come before the noun they modify, so the structure is Noun₁ がある Noun₂, meaning "Noun₂ that has Noun₁."
This is a natural extension of the basic sentence にわ庭がある ("there is a garden") used as a modifier for a noun. The clause before the noun works just like a mini-sentence describing that noun.
To express "a noun that does not have ~," replace ある with ない.
To describe something that had something in the past, use あった.