Running 'lean' means a weak fuel mixture i.e. not enough fuel to air mix. This is set by carburetor main needle valve. Symptons are engine overheating (which can cause damage) at full throttle the engine will gradually slow down. Flying will likely result in engine failure.
The engine carburetor should be tuned according to the manufacturers instructions. Generally this means starting rich and adjusting carburetor needle gradually until engine produces maximum power whilst still allowing small amounts of unused fuel to lubricate and cool.
An engine previously correctly tuned and running fine which begins 'leaning out' often indicates an air leak. e.g. hole in fuel pipe, damage to carb 'O'ring or missing carb fixing bolt/screw. All of which will allow unwanted air causing lean mixture. It can require a lengthy (and frustrating) process of elimination to identify the cause.
When flying as the tank is close to empty the fuel will begin to 'lean' out as the clunk on the fuel pickup tube in the tank scavenges more air and less fuel. The engine revs will increase particularly on diving, possible coughing of engine as fuel supply begins to be inconsistent. .