I'm about the same height as Tom.

Literal

I [topic-は] Tom [with-と] same-degree [possessive-の] back [possessive-の] height.

同じくらいの背の高さ ('about the same height') — 同じくらい ('about the same') + 背の高さ ('height' — literally 'tallness of the back'). と marks the person compared with. The final だ is the copula. A neutral comparison statement.