It can mean supervising or "directing" a research project or PhD thesis.
In daily life, "dirigir" is most commonly associated with operating a vehicle, though the nuance varies by region: Dirigir
It translates to "running" or "managing" a business or team (e.g., dirigir un negocio ). It can mean supervising or "directing" a research
The word "conduzir" is more common and formal, whereas "dirigir" is often reserved for directing people or organizations. Dirigir