。
She put on a coat and went out.
Literal
She [topic-は] coat [object-を] put-on [and-て] went-out-and-left.
出かけていった is a short stack: 出かける ('go out, head out') + the auxiliary ~ていく ('go off / move away from speaker'), itself in the past form. ~ていく reinforces the directional sense — she left the speaker's location, the action moved away. Compare to 出かけてきた ('went out and came back'). The opening clause コートを着て ('put on a coat and...') uses te-form chaining to set up the sequence: dress, then leave.