We did cover resilience briefly in prep course, but not much except 'some children are more resilient than others' and 'it is important to build resilience'. So on the one hand implying that it is a given, something that children come with (or don't); on the other hand implying that it is something we can affect/that was probably negatively affected in the past. I guess both bits are partially true.
I'd agree with Devora that it is similar to self-esteem.
For me resilience is about being able to come through bad things fairly intact. Not so much about avoiding bad things happening, but being able to come through them.
But what gives you that ability?
I guess you would be more resilient if you had a very secure sense of self, meaning a bad experience would not make you fundamentally doubt yourself.
Probably it has something to do with 'attribution style', a concept I came across about 15 years ago at uni, so no idea how up to date it still is; but basically if you attribute bad things to yourself (I'm rubbish hence this happened/I didn't achieve that) but good things to others/chance/things outside yourself (it is pure luck that I won that award, rather than 'I won it because I am smart', or 'I won it because I worked hard') then chances are you are not very resilient.
I can imagine that resilience has something to do with having an positive/optimistic attitude; seeing/expecting the good in something might help you get through an experience whereas you might struggle if you only saw/expected the bad. However over optimistic would not be good either as it would set you up to fail. So somewhere on the good side of realistic perhaps.
That prayer occurs to me, where you ask for the strength to change/improve the things you can change, the patience (?) to accept the things you can't change, and the wisdom to tell one from the other. I can imagine that this would make a resilient person.
I can also imagine that secure not only in yourself, but also in a network of people with shared values and shared feelings of belonging, would help you be resilient. If other people constantly validate you, you could deal with more trouble than if you lacked that background.
However how to help a child become more resilient… certainly no quick fixes! Time and consistency and reliability and a portion of luck thrown in I'd say.