이끌다 means "lead, guide, shepherd" 손을 이끌다 means "guide hand" 손을 잡고 이끌다 "lead somebody by the hand" e.g. 엄마가 아이의 손을 이끌고 가다.

이끌다 = 1) lead a person or group of people (on certain task or mission). 2) take a person along. (It is related to 끌다 which means to pull or attract. 이끌다 is like pulling someone to lead them in certain direction.) it usually takes a person or a group as its object, but it can also apply to someone's hand, arm, or sleeve, as in your example 손을 이끌다. - 지휘관은 사병들을 이끌고 적진을 향해 나아갔다 = The commander led the troops toward the enemy line. - 위기에 처한 나라를 이끌 지도자가 필요하다 = We need a great man to lead the country in crisis. - 어머니는 내 손을 이끌고 인파를 헤치며 나아갔다 = Mother took my hand and led the way through the crowd of people.