An accidental transposition of the initial sounds, or other parts, of two or more words. If you aren't familiar with spoonerismd this 'doctored' nursery rhyme should give you the idea:
Little Muss Miffet
Tat on a siffet,
Eating her words and kay.
A-spong came a lider,
And bat sown beside her,
And whitened Muss Miffet affray.
The Rev. William Archibald Spooner (1844–1930), who was a fellow and warden of New College, Oxford, is inextricably linked with the slips of the tongue that bear his name. Spooner was an albino and, more to the point for this piece, a sufferer of dysgraphia, which is a form of dyslexia that is characterised in the OED as 'a disturbance of the clear distinction of the sounds of words, confusion between closely related phonemes'. The albinoism may in fact have played a part in this as it is often associated with poor eyesight, which was certainly a symptom in Spooner's case.
Although his reputation for making what came to be called spoonerisms was widespread, most of the best known examples are inventions by others and it is impossible to tell which are genuine mistakes (by Spooner or otherwise) and which are made up for effect. For example, he is supposed to have said "I am a birdwatcher", which would un-spoonerise as 'I am a word botcher'. An excellent comic example should he ever have said it but, sadly, he didn't. The term 'spoonerism' was known colloquially in Oxford in his lifetime and was first written down in this piece from the London newspaper The Globe, February 1900:
To one unacquainted with technical terms it sounds as if the speaker were guilty of a spoonerism.
The good reverend gained both fame in his lifetime and linguistic immortality by the eponymous gaffes, which his otherwise unexceptional academic career wouldn't have brought him. Nevertheless, he didn't welcome his notoriety and in later life became rather cross about it. At a college dinner given in his honour on his retirement the undergraduates called for a speech; Spooner stood up and said, "You want me to say one of those things; but I shan't", and sat down.
As far as can be ascertained, the only example of a spoonerism actually said by Spooner is:
You will find as you grow older that the weight of rages will press harder and harder upon the employer.
He is also widely reported to have acknowledged coinage of 'The Kinquering Congs Their Titles Take' (in reference to a hymn) but I can find no convincing evidence of that admission.
Spooner's reputation must have come from somewhere and, although no doubt exaggerated by Oxford undergraduates who had developed a fashion for nonsense-speak in the late 18th century, he probably uttered other examples that went unrecorded. More reliable are the accounts of ideas or words that demonstrate the occasional transpositions caused by his mild mental disorder:
On one occasion he spilt salt on the tablecloth and poured claret on top of it.
On a tour of his college he remarked on the darkness of a staircase before turning off all the lights and attempting to lead a party down the stairs in the dark.
He asked an acquaintance "Was it you or your brother who was killed in the war?"
Commenting on another acquaintance he remarked "Her late husband, you know, a very sad death - eaten by missionaries - poor soul!"
Here's a list of spoonerisms that are often supposed to have been uttered by the reverend gentleman but come with the giveaway 'attributed to' label:
You have hissed all my mystery lectures. You have tasted a whole worm. Please leave Oxford on the next town drain. (You have missed all my history lectures. You have wasted a whole term. Please leave Oxford on the next down train.)
The Lord is a shoving leopard (loving shepherd)
A well-boiled icicle (well-oiled bicycle)
You were fighting a liar in the quadrangle (lighting a fire)
Let us raise our glasses to the queer old dean! (dear old queen, referring to Queen Victoria)
From Iceland’s greasy mountains (From Greenland’s icy mountains)
Dr. Friend’s child (referring to a friend of a Dr. Child)
Is it kisstomary to cuss the bride? (customary to kiss)
A blushing crow. (crushing blow)
Is the bean dizzy? (Dean busy)
Someone is occupewing my pie, please sew me to another sheet. (someone is occupying my pew, please show me to another seat.)
A nosey little cook. (cozy little nook).
As to spoonerisms unambiguously invented by others, they are legion. Here are a few:
Annual shower flow (annual flower show)
Bad salad (sad ballad)
Bat flattery (flat battery)
Bedding wells (wedding bells)
Belly jeans (jelly beans)
Birthington's washday (Washington's birthday)
Blushing crow (crushing blow)
Bowel feast (foul beast)
Britannia waives the rules (Britannia rules the waves)
Bunny phone (funny bone)
Cat flap (flat cap)
Chewing the doors (doing the chores)
Chipping the flannel (flipping the channel)
Cop porn (popcorn)
Crawls through the fax (falls through the cracks)
Damp stealer (stamp dealer)
Fight in your race (right in your face)
Flock of bats (block of flats)
Flutter by (butterfly)
Full bottle in front of me (full frontal lobotomy)
Guard hoeing (hard going)
Go help me sod (so help me God)
His nose was Roman; his grin pure cheek (chin pure Greek)
Hiss and leer (listen here)
Hypodemic nurdle (hypodermic needle)
I'm shout of the hour (I'm out of the shower)
Keys and parrots (peas and carrots)
Know your blows (blow your nose)
Lack of pies (pack of lies)
Lead of spite (speed of light)
Mad banners (bad manners)
Mad bunny (bad money)
Mean as custard (keen as mustard)
Mend the sail (send the mail)
My zips are lipped (my lips are zipped)
Nasal hut (hazelnut)
Nicking your pose (picking your nose)
No tails (toenails)
Pit nicking (nitpicking)
Plaster man (master plan)
Pleating and humming (heating and plumbing)
Ready as a stock (steady as a rock)
Rental deceptionist (dental receptionist)
Roaring with pain (pouring with rain)
Sale of two titties (Tale of Two Cities)
Sealing the hick (healing the sick)
Shake a tower (take a shower)
Sir Stifford Crapps (Sir Stafford Cripps)
Soppy cheese (choppy seas)
Soul of ballad (bowl of salad)
Tease my ears (ease my tears)
The rutting season for tea cosies (the cutting season for tea-roses)
This is the pun fart (this is the fun part)
Tons of soil (sons of toil)
Too titty to be a preacher (too pretty to be a teacher)
Trail snacks (snail tracks)
Wave the sails (save the whales)