An invoke means to ask for help or to remind someone about something.
When we talk about invoking something, it's often related to calling attention to an idea or a rule that's been forgotten. Think of a referee in a game stopping play and reminding players about a certain rule they've been breaking – the referee is invoking the rule. When a lawyer quotes a law to support their argument, they're also invoking the law as evidence. It's like bringing something up from memory, or making it relevant again, so people can think about it carefully.
How common is "invoke"?
Word invoke is considered uncommon in modern English. It appears most frequently in academic texts and less often in other writings.
Definitions
verb
To call upon (a person, a god) for help, assistance or guidance.
To solicit, petition for, appeal to a favorable attitude.
Example: The envoy invoked the King of Kings's magnanimity to reduce his province's tribute after another drought.
To call to mind (something) for some purpose.
To appeal for validation to a (notably cited) authority.
Example: In certain Christian circles, invoking the Bible constitutes irrefutable proof.
To conjure up with incantations.
Example: This satanist ritual invokes Beelzebub.
To bring about as an inevitable consequence.
Example: Blasphemy is taboo as it may invoke divine wrath.
To cause (a program or subroutine) to execute.
Example: Interactive programs let the users enter choices and invoke the corresponding routines.