。
She bought a dance music record.
Literal
She [topic-は] dance music [genitive-の] record [object-を] one-flat-thing bought.
一枚 uses the counter 枚 — the classifier for flat, thin objects (paper, photos, plates, shirts, tickets, CDs, vinyl records). Japanese requires a counter when stating quantity: 'one record' must be レコードを一枚, not レコードを一. The whole sentence string ダンス音楽のレコード stacks three nouns with の to form a single concept ('dance music record'), which is how Japanese builds compound noun phrases that English would render as 'X-Y-Z.' Several Western dance forms entered Japanese as direct loanwords during Meiji-era westernization (ワルツ, タンゴ, ジャズ), and this kind of katakana-heavy phrase has the breezy, mid-20th-century feel that goes with that lineage.