。
She pulled the chair toward her.
Literal
She [topic-は] her own direction [toward-に] chair [object-を] drew-near.
自分のほうに ('toward herself, toward her direction') uses ほう (方, 'side, direction') as a pseudo-spatial noun marking a direction relative to the subject. に marks the destination of the motion. 引き寄せる (引く + 寄せる, 'to pull + to bring near') is a compound verb meaning 'to draw something close, pull near.' Common in scenes of physical adjustment — moving objects in a room, drawing someone in, pulling a chair forward to sit.