Doublets are a type of close-fitting jacket. They were popular from the late 14th century to during the Renaissance. They may or may not have sleeves, which could be laced on and detachable, or fixed to the garment and the point where the sleeve joined the torso was smaller than modern garments.
Doublets often contained holes on the hips to which laces were tied to hold up a man's hose.
They continued to be used in the 17th century where they had become the outer garment (previously they were typically worn under a coat or gown). Doublets of this era did not appear to have detachable sleeves.