Order of error occurrence

1. All validation errors run at same time whether error defines top of page or on field
2. Errors that are defined or come due to trigger  come in last order i.e an error that is in last of apex execution notifies first to the user. 

Validation Rule

Define a validation rule by specifying an error condition and a corresponding error message. The error condition is written as a Boolean formula expression that returns true or false. When the formula expression returns true, the save will be aborted and the error message will be displayed. The user can correct the error and try again.


Note:
Validation Rules fire only on insert,update,upsert not on delete and undelete