The British phrase the penny dropped is used to indicate that someone has finally understood or realised something.

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It was originally used with allusion to the mechanism of a penny-in-the-slot machine. The following, from The Leeds Mercury (Yorkshire) of 30^th August 1911, evokes this mechanism:

PAPER PENNIES.
OTLEY LAD’S PRANK WITH AUTOMATIC MACHINE.

A number of imitation pennies made of paper were produced in the Otley Police-court yesterday, in a case in which an Otley schoolboy, Teddy Paley, was charged with stealing two packets of chocolate from an automatic machine.
It was stated that the machine was placed at the door of Mr. Thos. Coates’s shop in Station-road, Otley. Mr. Coates said he had suffered during the past twelve months through boys inserting these paper pennies and also various kinds of base coins, brass checks, and tins. He could hear from the shop when a penny dropped, and as there was no sound when these paper coins were put in, he went to the door and found Paley in the act of taking out the chocolate. Four paper coins were inside the machine.
The lad’s father said his son had got into bad company. He had been to Guiseley with a boy, who had showed him how easy it was to get chocolate from these machines.
Paley, who expressed penitence, was bound over for twelve months, and placed under the care of the Probation Officer.

Vintage bally slot machines. Gas in particular used to be supplied to certain consumers on the automatic penny-in-the-slot principle. One of the earliest mentions of this that I have found is from The North-Eastern Daily Gazette (Middlesbrough, Yorkshire) of 4^th September 1890:

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THE “PENNY IN THE SLOT” GAS SYSTEM AT BOLTON.

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The Bolton Corporation are now supplying gas on a novel principle. There are 7,000 houses in the town not using gas, though they have fittings. Most of these dwellings are occupied by artisans and workers of a poorer class, and their custom is sought as gas consumers in this way—each tenant, by putting a “penny in the slot” of a machine provided for the purpose, is supplied with 25 cubic feet of gas.

By 1890, penny-in-the-slot machines had become all the rage, to the extent that penny in the slot was a proverbial phrase; there were for example automatic postal boxes supplying postcards and stamped envelopes with paper enclosed, automatic insurance boxes providing an insurance for 24 hours against accidental death, and automatic photographic machines that The Pall Mall Gazette (London) mentioned on 8^th May 1890:

REVOLUTION IN PHOTOGRAPHY.
A PHOTOGRAPH DELIVERED AUTOMATICALLY IN 45 SECONDS IN EXCHANGE FOR A PENNY.

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The Press of the kingdom declare the invention “marvellous.”
TRUTH.—I am told that before long we shall have the Automatic Photographic Camera on the streets and in the Railway Stations. A friend who inspected the Machine at Messrs. Salters, West Bromwich, the other day, informs me that the likeness is taken within three seconds of dropping the proverbial penny in the slot, and that the complete picture is delivered in about 30 seconds. In point of speed, at any rate, this beats Mr. Weller’s “profeel machine.”

AUTOMATIC PHOTOGRAPH COMPANY (Limited).
PROSPECTUSES WILL BE READY ON SATURDAY NEXT.

The earliest figurative use of the penny dropped that I have found is from On getting educated, published in The Ripley and Heanor News and Ilkeston Division Free Press (Ripley, Derbyshire) of 10^th April 1931:

One of the advantages of walking is that one makes a lot of interesting and informative contacts.
[…]
One pleasant autumn afternoon I was approaching Cromford via Lea (and what a lovely old bridge the one at Cromford is) when I saw a fragile-looking man leaning on a gate.
“You don’t look very grand,” I said. “Can I help you in any way?”
“No, thank you kindly. I’ve got a new complent. What’s squealers, mister?”
“The only squealers I know are pigs,” I replied. “Where’s the trouble?”
“You see, sir, I’ve had bronikle pneumonia, but I got over that, and yet I couldn’t get about, so my missis her axed doctor what was matter with me now. The doctor he said, ‘Oh, he’ll get right in time; he’s got squealers.’”
Then the penny dropped and I realised what it was.
So I said to him, “Yes, I know what it is. You are short of breath and always feel tired, I expect.”
“That’s just it, mister. Then it isn’t serious?”
“Not if you take care of yourself,” I replied.
“There’s one thing as does me good,” he went on, “and that’s a thimblefull of brandy, but I’m spent up.”
So we arranged matters.

The second-earliest instance that I have found is from the Skegness Standard (Skegness, Lincolnshire) of 20^th April 1932:

THINGS WE WANT TO KNOW.
The identity of the gentleman who was allowed to go for a drink after assisting the missus on Sunday?
And how long it took him to fathom the problem as to why the hostelry was closed at 1.15 p.m.
And if the penny dropped on suggestion of his spouse that he had forgotten to advance his watch an hour?
And if he has made a mental resolve to guard against a similar happening in future years?

The following is from the Derby Evening Telegraph & Derby Daily Express (Derby, Derbyshire) of 1^st July 1932: Slot machine for sale lightning link.

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“She was only a gasfitter’s daughter, but she had slots to meter,” may have been a very good joke, but it took my wife a long time before the penny dropped