First, it is important to realize that not all cells are "immortal." Most normal cells age, stop reproducing, and eventually die. Think of normal cells like our human bodies. For some reason, Henrietta's cells (HeLa cells) did not follow this same pattern.
According to AccessScience,
Unlike normal body (somatic) cells, HeLa cells thrive indefinitely in laboratory tissue cultures, a trait that has allowed them to assume tremendous importance in biomedical research.
In addition to being immune to aging and death, these cells are very strong. Where a normal cell might easily die when being exposed even to air, HeLa cells do not.
So, science considers these cells immortal because they literally do not die.
Why then is this important? Well, if you think of cells as being a resource that scientists always need a lot of at any given point, it only makes sense that having a cell line that never dies is a lot more efficient than having to constantly procure other cells. Also, using the same cell line again and again provides the scientitsts with a built in control as well.