'Yes,' Nora said, feeling like a spy about to have her cover blown.

[shootingstar]

(Nora becomes engrossed in a new life she is thinking of, half dreaming half being awake)
. . .
Then a spindly twenty-something man in a baggy rugby top popped up from behind the bar, hardly giving any attention to Nora as he gathered the lastremaining used glasses and put them in the dishwasher. He switched it on then pulled down his coat from a hook, put it on and took out some car keys.
'Bye, Nora. I've done the chairs and wiped all the tables. Dishwasher's on.'
'Ah, thanks.'
'Till Thursday.'
'Yes,' Nora said, feeling like a spy about to have her cover blown.

(The Midnight Library by Matt Haig, episode The three Horseshoes)

I understand the set phrase "blow someone's cover", however I don't know the correct meaning of "cover" and of "blow" in this phrase. What exactly do they mean?

 

[jutfrank]

One sense of the verb 'blow' is something generally similar to 'ruin'.

You totally blew it!
She blew her only opprtunity to escape.

The word 'cover' in this general sense means being unseen or in disguise. It's often used therefore in police and military operations, as well as espionage. If you're a spy, under cover, you obviously don't want anyone to find out. The 'blow/ruin' part applies then to people finding out. If they do, your cover is blown.