。
The lovers carved their initials into the oak tree.
Literal
Lovers [topic-は] their-own [of-の] initials [object-を] oak [of-の] tree [in-に] carved.
自分たち is the reflexive 'one's own (selves),' which here clarifies whose initials are being carved. 頭文字 literally 'head-letters' = 'initials, first letters of names.' The に on かしの木に marks the goal/destination of the carving — where the initials end up. かし is 'oak' (kanji 樫), here written in kana.