Solid responses here. I'll add a partial definition:

Being in a position where it is extremely difficult, if not seemingly impossible to care for basic needs or to get the help necessary to do so. E.g. due to financial insolvency and lack of access to social security nets).

This applies regardless of whether one recognizes the necessity of seeking help, because I believe that some human needs are universal (e.g. food, sleep, medication, shelter, etc). One is in a crisis (in my opinion) if these things are lacking in a quantity and quality necessary for healthy survival, regardless of whether one recognizes the lackings.