In older carburetor-equipped cars, depressing the accelerator before starting helped to:
* Prime the carburetor: Carburetors rely on a mixture of air and fuel. Depressing the accelerator would open the throttle plate, allowing more air to flow. This, in turn, could help draw fuel into the carburetor, improving the chances of a smooth start, especially in cold weather or after the engine has sat for a while. A properly functioning carburetor should generally not require this, but it was considered a helpful trick.
* Bypass the choke (sometimes): Some carburetors had a choke system that restricted airflow to enrich the fuel mixture for easier cold starting. Depressing the accelerator might partially or completely disengage the choke, allowing a richer mixture to be drawn in.
Modern vehicles with fuel injection systems don't require this. The fuel injection system electronically controls the fuel-air mixture precisely, negating the need for manual priming or choke adjustment. Attempting to depress the accelerator before starting a fuel-injected car is unnecessary and might even interfere with the engine's computer system's attempts to start the engine properly.