She gave me a leather handbag.

Literal

She [topic-は] leather-made [attributive-の] handbag [object-を] gave-to-me.

革製 ('leather-made') uses the productive suffix ~製 ('made of / produced in / manufactured by') for material or origin: 紙製 ('made of paper'), 日本製 ('made in Japan'), 木製 ('wooden'). When attached to a material it specifies what the item is made from. The の links 革製 attributively to ハンドバッグ. くれる ('to give to me / us') is the speaker-side verb in Japanese's three-way giving system: あげる ('give outward'), くれる ('give inward to me/my group'), もらう ('receive'). The choice of くれる here registers the gift-giving as personally directed at the speaker, with implicit gratitude built in. The kanji 革 specifically refers to tanned leather, distinct from 皮 (skin in general).