This is the 5983rd most frequent Japanese word.
アジアン
"Asian" (pertaining to Asia or Asian style).
アジアン in this sentence is used as an adjective to describe the style or atmosphere, imparting a sense of 'Asian-inspired' ambiance.
彼のインテリアのセンスはアジアンな雰囲気がある。
His interior design sense has an Asian vibe.
アジアン is used here as an adjective describing 'cuisine' or 'food' as being Asian in style or origin.
アジアン料理が好きです。
I like Asian cuisine.
アジアン modifies 'マーケット' (market), specifying it as an Asian-style market or one selling Asian items.