。
She's reluctant to get married.
Literal
She [topic-は] marry [nominalized-のを] is-showing-dislike.
嫌がる is the verbal form of 嫌 ('dislike'), describing visible signs of dislike rather than the inner feeling itself — same pattern as 怖い → 怖がる, 欲しい → 欲しがる. The choice to use 嫌がる instead of plain 嫌 reflects Japanese's general avoidance of asserting someone else's inner states directly: a third party's feelings are inferred from outward behavior. The nominalizer の turns 結婚する into a noun phrase that を marks as the object of 嫌がる. Combined with ~ている for the ongoing/sustained reading, the whole structure delivers 'has been showing reluctance about getting married.'