What's the meaning of the phrase 'Stuck fast'?
To be stuck fast is to be firmly fixed in place and unable to move.
What's the origin of the phrase 'Stuck fast'?
The OED lists eight different meanings of the word fast, so to understand the expression 'stuck fast' we need to decide which fast we are talking about. As it happens, it is number five on the list and their unambiguous definition is 'Fast - Firmly fixed in place; not susceptible to disturbance or displacement; stable, stationary.'.
In recent months (April 2020) their have been a couple of news stories where the journos have reached for the phrase 'stuck fast'. The first was the blockage of the Suez Canal in March 2021 by the container ship the Evergreen. If ever a ship was stuck fast is was that. The second is the more recent (March 2022) discovery of Ernest Shackleton's ship Endurance beneath the Weddell Sea. The ship was stuck fast in the ice for some time before sinking in 1915.
Although it is still pressed into service on modern-day news reports it turns out that the phrase itself is very old. The first record that I can find of it is in William Caxton's printing of The Golden Legend, 1493, in which he describes the bringing of Christianity to England by Saint Austin:
And thenne Saynt Austyn toke hys staffe for to remeue fro that place and sodeynly his staffe sprange out of hys honde with a grete vyolence the space of thre furlonges thens and there styked faste in the erthe.
[Then Saint Austyn took up his staff to leave and suddenly the staff sprang out of his hand with great violence, flew three furlongs and stuck fast in the ground.]
Note: A furlong in Caxton's day wasn't a fixed distance and varied from place to place. These days it is standardised as 220 yards.
See also the related expression 'hard and fast'.