On a cloud architecture (but in general on every IT system), you could have different events that could cause a failure of your solution. These failures could have a totally different nature, they could be hardware-related (a server goes down, a disk is corrupted and so on), they could be network-related (network glitches) or they could be data center-related (imagine a big problem on a data center or an Azure region).

When designing an architecture for the cloud, you need to have in mind that your solution could be affected by failures and you need to react to those failures, as soon as possible. This is the concept of Resiliency.

For a system, Resiliency (as a definition) is the ability to react to failures and continue to work. I've placed in evidence the word react because it's extremely important. You cannot totally avoid failures (some of them are totally unpredictable and not dependent on you), but you need to plan for a solution architecture that responds to failures...