Something that fails ignominiously to satisfy expectations; an anti-climax, a disappointment.
The first thing to say about the expression 'damp squib' is that is is 'squib', not 'squid'. Squid are a species of cephalopod. In their natural environment squid are usually damp but that's as near to this phrase as they are likely to get. Having mentioned squid I ought also to get the other notable squiddish play on words out of the way - the old joke "Hey, where's that sick squid you owe me?". Having done our linguistic duty with squid, we can now move on to 'damp squib'.
A squib is a form of firework, usually cylindrical in shape with a paper fuse at one end, which provides a mild explosion - think 'dynamite lite'. Clearly, fireworks work best when they are dry. Anyone who, at a backyard bonfire, has lit the blue touch paper and retired only to see the firework phut and fizzle out will know the disappointment of a damp squib.
In the 16th century, 'squibs' were also short, sharp literary compositions of a satirical or sarcastic character. Both the 'firework' meaning and the 'satire' meaning are first found in print in the 1520s and it isn't entirely clear which came first.
The first use that I can find of the expression being used figuratively certainly derives from the 'firework' meaning. That is in the London newspaper The Morning Post, March 1837, in a complimentary article about the British parliamentarian George Grote:
Mr. Grote is a nice man. We rather like Mr. Grote. Mr. Grote does not vote black white; or fiz and splutter, after the fashion of a damp squib.
'Squib' isn't a word that we find ourselves using very often, hence the erroneous 'damp squid' isn't difficult to find in print, for example, this piece from the Trinidad & Tobago Express, June 2005:
I imagine the excitement will last for another few weeks before it peters out into a damp squid...