Aria is a musical term first used to identify any expressive melody, usually (but not always) performed by a singer. Later on, same term described a standalone piece of vocal music (for one voice) accompanied or not by orchestra, normally a part of a larger work. Arias along with recitatives are an integral part of opera. They are also found in oratorios and cantatas. Some composers, like Beethoven and Mozart have also composed concert arias.
Aria da capo
Was the most prevalent form during Baroque period. A soloist was singing with instrumental accompaniment, usually a small orchestra. It was was used in opera and oratorio very often.
The form is ABA. First part, written in tonic, could stand alone . The second part contrasted with the first, in terms of tonality, mood and (sometimes)tempo. Usually, composers did not compose a third part; instead they gave a direction "da capo" (from the beginning).
The term "Aria is sometimes used in contemporary music as a title for instrumental pieces, e.g. Robin Holloway's 1980 'Aria' for chamber ensemble.