。
She spread a pretty cloth over the table.
Literal
She [topic-は] pretty cloth [object-を] table [of-の] top [on-に] spread.
Two structural pieces. テーブルの上に uses 上 ('top') as a relational noun — connected with の to the noun being located and に for the destination of the action. This compound-particle system (~の上に, ~の下に, ~の中に, ~の前に) is how Japanese builds spatial relations from a small set of common nouns plus particles. 広げる ('spread out, open up, lay out') is the transitive partner of 広がる ('spread out, become wide'); 広げる takes a direct object (the cloth being spread), while 広がる describes the spreading itself happening.