Imagine that you are walking along a street with shops on either side. You walk quickly along the pavement (sidewalk) from number 2 to number 10 without stopping. If you do this, you go past the shops at numbers 4,6 and 8. You don't stop at these shops - you go past them. On the other side of the road, you see a shop that looks interesting. So you have to go across the road in order to reach that shop.

If I go past the park, I don't enter the park, I walk alongside it. If I go across the park, I enter the park and exit the other side.