In general, you want your soil to have acidity between 6.5 and 7.0 pH. Too high, and the soil is alkaline, or "sweet." Too low, and the soil is acidic, or "sour." Either extreme is bad for your lawn.
Lime is a calcium-based chemical that reduces the acidity of soil that has a pH level below 6.5. The further below 6.5 pH the soil is, the more lime benefits it.
Three types of lime give you a choice for raising pH. Ground limestone, or calcium carbonate, is the cheapest and also the safest to handle. Burnt lime (CaO) works must faster, but is also caustic and can damage skin. Hydrated lime (Ca(OH)2) sits in the middle: not as harsh as burnt lime but faster than ground limestone.