Children understand division on a very practical level. How many x do we have, and how many y do we have to share it between? They may apply it to cookies, slices of bacon, play silks, or wooden blocks. There is a strong desire for things to be divided in an even and fair manner. Written division takes this process from the concrete to the abstract. When we worked simple division and division with remainders we used manipulatives and then a bridge to bring it from the concrete (rocks in our hands) to the abstract (numbers and symbols written on paper).
When talking about long division with the boys, even with two digit divisors, I often bring the abstract problems back into the practical by asking the question the same way I would if I had 10 pieces of bacon for 4 people; only the numbers get bigger. I have 169 wooden blocks and 13 children to share them. There are 1248 M&Ms and 48 children to share them. Talking this way makes the problems something that the child can understand.
Again, using grid paper is very helpful with long division, as the columns stay nice and tidy. We also use a sticky note to cover the parts of the equation that we aren't working with. Together these help the child see the problem clearly and work the steps in order.