What is running lean and running rich?

"Rich" and "lean" refer to the air/fuel mixture. Rich means a higher proportion of fuel than is needed and lean means less.

An overly rich mixture can foul plugs, cause sluggish performance and promote carbon buildup in the combustion chambers, as well as decrease fuel economy.

An overly lean mixture can cause jerky, hesitant performance, overheating and in extreme cases even melt a piston crown.