Persian بوستان (bôstân) is also the source of Classical Syriac ܒܘܣܬܢܐ (būstānā), and perhaps of Old Armenian բուրաստան (burastan, "garden; orchard; suburb"), which would otherwise usually considered to be formed natively in Armenian as բոյր (boyr, "smell, odour") + -աստան (-astan, "place forming suffix, as in all the Central Asiatic Stans [Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan and Uzbekistan]").
Looks like we are talking about ornamental grounds laid out for public enjoyment and recreation. I'm British, but I think this meaning of "garden" also applies in American English.
I believe that both variants of English also use the word "garden" in the sense of a place to grow your own vegetables, fruit or flowers, but it looks like "shamba" might be the specific word for vegetable garden in Swahili, with "bustani" meaning public, manicured, ornamental garden.
Hmm, it looks like another occurrence of “bustani” in the course is “bustani ya matunda,” less than completely helpfully translated as “garden of fruit” (“orchard” maybe?). It would seems that’s more likely to be a place where the primary point is the crop, as opposed to the ornamentation, but of course it’s hardly dispositive.
Just as long as it doesn’t mean what an American would call the “back (or front) yard” :) (which is where the dialect stuff gets really confusing)