Cell immortality is a phrase that biologists use to describe cells that can infinitely divide given proper nutrition. Please note that we have said, we have given proper nutrition. For instance, cancer cells are primarily known as immortal cells. These cells can continuously divide when provided favorable nutrition in vitro and in vivo. However, as seen in vitro, the cancer cell lines also die when nutrition is completely used up in the media.

Now, you would say, "What if we replace the media?" If we change or provide fresh media once these cells have reached their limit, then they will not divide. Interestingly, we provide media to them before they die, and then these cells will bounce back and revitalize. So, we can say that an immortalized cell or cell line will be able to live if it is provided with sufficient nutrition.
As for the cancer cells, there are several reasons that researchers have found that make them immortal. All the factors primarily change how the cell cycle is regulated to enable cells to continuously divide. In other words, we can say these cells are undergoing uncontrolled division, giving us the illusion of immortality.

(Image Source: https://www.researchgate.net/figure/Human-MSC-immortalization-method-including-SV40LT-and-hTERT-retroviruses-produced-by_fig1_342233211)

In research, when we need to convert any primary cells to immortalized cells, we require that we provide these cells with the immortality gene "Telomerase" (hTERT). This gene does not disrupt the physiological environment of these cells but enables them to divide multiple times more than if the gene were not present. Hence, cell immortality is a concept that allows us to produce a large number of a particular cell type.