She's in the middle of writing a letter.

Literal

She [topic-は] letter [object-を] writing [in the middle of-ところです].

~ているところ (in the middle of doing) captures a snapshot of an action in progress. ところ (place/moment) here refers to a temporal 'place' — the moment of doing. Adding です makes it polite. This pattern emphasizes that the action is happening right now, more vividly than plain ~ています, which could also mean habitual action.