Grading refers to sloping your yard away from the foundation of your home so any excess water will drain properly and away from your home. This not only helps prevent the lawn from becoming waterlogged in spells of heavy rainfall but also protects your house and its foundations from potentially damaging exposure to excess moisture.
Leveling your lawn or yard area refers to making the surface area smooth and bump-free. While primarily aesthetic, leveling your lawn can also help to prevent other problems like improper drainage, pooling (which can lead to outbursts of weeds and attract mosquitoes), and scalped areas where your lawnmower blades scrape over bumps or hillocks.