Keys to the city

So Bloomberg has awarded "keys to the city" to Captain Sullenberger
and his crew for their heroics and amazing feat of landing Flight 549
beautifully with no lives lost or major injuries. What the heck are
"keys to the city"?! Is this literal or figurative or both? Can the
Cpt unlock the doors to Gracie Mansion? Go to the Bronx zoo after
hours? Get to the head of a line at the DMV? Get into a Yankee game
for free? Etc. I'd like to know exactly what is proffered by this
privilege and why every journalist assumes I know because I have no
clue.

UPDATE - I found this website defining keys to the city.
Still pretty murky to me. Says that "...the recipient is as free to come and go at will." When, where, what, how?!