The phrase "strong emphasis" means to place a great deal of importance or stress on something. It is used to indicate that something is being said with strong conviction, forcefulness and urgency. The word "emphasis" refers to the act of drawing attention to something by giving it more prominence or highlighting its significance. When emphasis is described as "strong," it implies that the speaker is placing particular importance on what they are saying in order to convey a sense of urgency, seriousness or insistence.