。
I moved a piece one space forward on the board.
Literal
I [topic-は] board [of-の] top [of-の] piece [object-を] one-[counter-つ] forward [to-に] advanced.
Board-game narration continuing from the chess context. 進める is the transitive counterpart of 進む 'to advance' — Japanese marks the distinction grammatically: 進む 'X advances (on its own),' 進める 'advance X (make something advance).' 一つ前に 'one (step) forward' uses the counter 一つ for general small units. 駒 is the word for a game piece (chess, shogi, go).