simple. living organisms share one common thing - DNA or RNA. to support basic function, it is necessary to replicate it and to read it in order to build proteins and other things. this processes are almost perfect, but there is always a small chance that they go wrong. if these mistakes accumulate, the basic functions will eventually break down and cause the system to collapse.
take the human body for an example. all the time, cells are destroyed and new cells grow in order to keep the body alive. theoretically, a human body does not have to die, as long as new cells gro and old cells die. so, if the human doesn't die from being damaged, it can live forever.
but the problem lies in the division of the cells itself. the process of copying the dna is almost perfect, because it has even mechanisms to repair damages and avoid errors during the process. but with many billion divisions during the lifespan of the organism, the probability of errors occuring increases more and more. so, theoretically a being doesn't have to die, but in reality, it's impossible to survive forever.