She has the advantage over me.

Literal

She [topic-は] me [than-より] is-advantageous.

The particle より marks the basis of comparison — 'than X / compared to X.' XはYより~ is the canonical comparative frame: '[X] is ~ compared to [Y].' Here 私より sets the speaker as the standard against which she is being compared. 有利だ ('advantageous, in a favorable position') is a な-adjective that takes its target with に (私に有利 'advantageous for me'), but here the comparison is structural rather than directional, so より does the work alone.