The word "catastrophe" has a particular set of associations in the history of aging science, as Chris Patil notes over at Ouroboros:
The idea that translation fidelity might play a role in aging dates back at least as far as 1963, when Leslie Orgel proposed the "error catastrophe" theory of aging: in this model, mistranslation of the translational machinery creates a feedback loop that leads to further translation errors, ultimately causing loss of cell viability.
All the machinery in a cell is made of protein components, including the machinery that makes those protein components: DNA is first transcribed into RNA, which is then translated to make the protein specified by DNA. Errors in the translation portion of a self-replicating machine are not a good thing - who knows where you'll end up as flaws are introduced and cascade into more flaws.
Error catastrophe was a nice theory while it lasted, but it doesn't in fact appear to be significant in mammals; we have exceptionally reliable genetic machinery. So good that across a lifetime you won't see anywhere near enough errors to kick off this runaway feedback catastrophe.
The (largely settled, largely historical) debate over the error catastrophe theory bears more than a passing resemblance to the present debate over stochastic mutations in DNA itself. While there is a consensus that accumulating random DNA damage (mutations in single genes in single cells) leads to cancer, it is less certain as to its contribution to other aspects of aging. On the one side, there are researchers who think that DNA mutations scattered throughout your cells causes much of age-related degeneration and dysfunction, and on the other side are researchers who think that it isn't all that important outside of cancer. Like the error catastrophy theory, this debate is one that will be settled in the not too distant future through advancing biotechnology and good measurement.
The error catastrophe theory is still an important waypoint in the evolution of theories of aging, and it has had tremendous influence in other areas within biogerontology. For example, similar logic has been applied to the role of autophagy in aging, where the feedback loop is called the garbage catastrophe.
The essence of the garbage catastrophe is that too much of the wrong sort of garbage can slow down or otherwise degrade the process of removing all garbage - so things will very quickly accelerate off the cliff once the loop kicks into high gear. For more on one way in which our cellular garbage collection mechanisms are damaged over time you might look at the LysoSENS background at the SENS Foundation:
Cells have a lot of reasons to break down big molecules and structures into their component parts, and a lot of ways to do so. Unfortunately, one of the main reasons to break things down is because they have been chemically modified so that they no longer work, and sometimes these chemical modifications create structures that are so weird that none of the cell's degradation machinery works on them.
This situation is very rare, but in the long run these modified chemicals add up. Ultimately the chemicals end up in the lysosome, a special vessel that contains the most powerful degradation machinery in the cell. If something can't be broken down there, it just stays there forever. This doesn't matter in cells that divide regularly, because division dilutes the junk enough that it remains at harmlessly low levels, but non-dividing cells gradually fill up with this stuff, making them dysfunctional. The heart, the back of the eye, some nerve cells (especially motor neurons) and, most of all, white blood cells trapped within the artery wall all suffer from this.
Catastrophe theories are actually a good thing if proven. We want aging to work through feedback loops that run at low levels for a long time before accelerating at the end: this is the ideal sort of machinery in which to intervene. In LysoSENS for example, the plan is to safely break down the biochemical gunk that's clogging up the works via the introduction of bacterial enzymes. Provided you remove that part of the loop before things get very out of hand and cause dramatic damage elsewhere, you've effectively reset the clock.