You have a great activity planned using the laptop cart and your network is down.
A resilient teacher can usually quickly redirect to a new or modified activity and learning will still take place, whereas, a non-resilient teacher may experience quite a bit of panic!
Your go-to online program for managing student work has decided to shut down.
A resilient teacher will shrug their shoulders and start searching for a new, perhaps better, program that they can use and start learning about it, while a non-resilient teacher will just give up and go back to pencil and paper.
Your district switched to a different productivity platform (like Office 365) that you are unfamiliar with.
A resilient teacher will take advantage of this new opportunity and seek out PD to see how it can benefit themselves and their students while a non-resilient teacher will growl and refuse to give up the old one or just not bother learning the new one.
Of course, these are just a few broad examples that I have encountered either personally as a teacher or in working with other teachers. The primary difference in resilience and non-resilience is your willingness to embrace change. I consider myself so fortunate to have worked with so many educators who are willing to do this, one in particular! It makes my work as an Instructional Technology Coordinator much more meaningful and it is my hope that a "digital resiliency fever" will take over education very soon!