。
She's right in the middle of having dinner.
Literal
She [topic-は] dinner [object-を] [is-eating-食べている] [middle-ところ] is.
~ているところだ pinpoints a moment in progress — 'is right in the middle of doing X.' Sharper than plain ~ている: where ~ている could mean 'has eaten and is now in the post-state' or 'is eating right now,' adding ところ ('place, point') focuses on the immediate ongoing moment. ところ extends from its concrete meaning ('place') to abstract use as a temporal pinpoint — a small piece of grammaticalization that gives Japanese aspect its precision. ディナー is a loanword used for relatively formal or Western-style evening meals; in everyday speech 夕食 (yūshoku) or 晩ご飯 (banhan) would be more typical.