。
She loves Tom more than she loves me.
Literal
She [topic-は] me [than-より] Tom [of-の] side [object-を] is-loving.
The frame X より Y の方を [verb] ('do [verb] to Y more than X') uses the comparative より to set the lesser member, then の方 (literally 'side') with を to mark the preferred one as the action's object. 方 ('side, alternative') is one of Japanese's standard ways to single out one option in a comparison: ~の方が好き ('prefer X'), ~の方がいい ('X is better'). 愛している, with the resultative ~ている, marks an ongoing emotional state — 'is in love with,' not just 'loves at this moment.'