put a little elbow grease into it

Put a little elbow grease into it is another way of being told to do hard work, especially in terms of cleaning something as in this instance you will be using elbow grease. Elbow grease is often the phrase used for cleaning something, because if it was very dirty you literally got grease on your elbows. To be told to put elbow grease into it, it means to work very hard at it and usually pertains to some sort of cleaning or chore.