"In the old way of doing things, we treat our servers like pets, for example Bob the mail server. If Bob goes down, it’s all hands on deck. The CEO can’t get his email and it’s the end of the world. In the new way, servers are numbered, like cattle in a herd. For example, www001 to www100. When one server goes down, it’s taken out back, shot, and replaced on the line."
This is a pretty good in depth explanation, but at a high level if a your server dies and you are extremely upset about it (similar to if your pet died) you are putting too many eggs in that single basket, with no secondary plan. Conversely if you build your infra in such a way that your server dying is something you see no worse than how a farmer sees one of his cattle dying (which are raised to be killed) - you are much better prepared for the inevitable downtime from your server and can very easily recover
