Leaf through implies a rapid or casual way of looking at the pages, not reading in detail. I leafed through the cookbook looking for a recipe that caught my eye.
Pro Tip 2/3
No Deep Reading
When someone leafs through a publication, they often won't remember specifics because they're skimming. She leafed through the manual but later couldn't find the information again.
Pro Tip 3/3
Physical Action
Leaf through usually involves using fingers to turn multiple pages, highlighting the physical aspect. During the meeting, he leafed through his notes nervously.