Refer to figure.
The priming system consists of a priming pump that will deliver fuel to the induction manifold. Its whole purpose is to inject additional fuel in the cylinder's intake ports to assist the engine start. In the absence of such a system, it is possible to deliver more fuel to the cylinders by pumping the throttle lever which will act on the accelerator pump and deliver more fuel. The priming pump will be fitted in parallel with the main fuel pump (which is either electric or mechanical) and will take fuel from the filter housing and channel it to the inlet manifold.

The necessary amount of priming required will mainly depend on the ambient temperature and how long the engine hasn’t been running. Priming is mostly necessary for the first flight of the day and during cold weather after the engine has been off for a few hours (depending on the engine type). However, sometimes it is not even needed as the engine will perfectly start without priming. Over-priming a hot engine could lead to a buildup of excessive fuel inside the cylinders, potentially increasing the risk of an engine fire, flooding the engine, and fouling the spark plugs.

The primer pump is supposed to be locked after start, however, leaving the primer pump open leads to a large increase in the amount of fuel allowed into the intake, and enriches the mixture significantly, to the point that the engine will run more roughly, cause a large amount of fouling on the plugs, and may even cause a "rich cut", where the engine stops, effectively due to lack of air due to the mixture being way too rich. This should be noticed during the power checks, but if it happened in-flight then you should notice also.