She took a lot of luggage with her.

Literal

She [topic-は] luggage [object-を] a-lot carried went.

持って行った (carried and went) uses the directional compound ~ていく — motion away from the speaker's location. 手荷物 (てにもつ) means hand luggage or carry-on bags: 手 (hand) + 荷物 (luggage). たくさん (a lot) describes the quantity. The ~ていく pattern here is literal: she physically carried items away from here.