The phrase things that go bump in the night denotes ghosts or other supposed supernatural beings, regarded as the cause of unexplained or frightening noises heard at night.

This phrase has its origin in a prayer of deliverance first recorded (in various forms) in the early 20^th century; the earliest instance that I have found is from the preface to The Magic Casement: An Anthology of Fairy Poetry. Edited, with an introduction, by Alfred Noyes¹ (London: Chapman and Hall Limited, 1908):

“And if that the bowle of curds and creame were not duly set out for Robin Good-fellow, why, then, ’ware of bull-beggars, spirits,” etc.
“From Ghoulies and Ghoosties, long-leggety Beasties, and Things that go Bump in the Night,
     Good Lord, deliver us!”
                              Quaint Old Litany

¹ Alfred Noyes (1880-1958), English poet, short-story writer and playwright

An early reference to the prayer (in an altered form and without quotations marks) appears in the unsigned review of How I know that the dead return, by William Thomas Stead²—review published in The Los Angeles Times (Los Angeles, California) of Sunday 10^th October 1909:

From now on, I refuse to read any more ghost stories. I am done! No more spook propaganda for me. No books on goblins, long-leggety ghosties, or things that go bump in the night, will find a reader in me.

² How I know that the dead return (Boston, Massachusetts: The Ball Publishing Company, 1909), by William Thomas Stead (1849-1912), English newspaper editor and spiritualist, who died in the Titanic sinking

The British author George Oliver Onions (1873-1961) prefaced his collection of ghost stories Widdershins (London: Martin Secker, 1911) with the prayer:

“From Ghaisties, Ghoulies and long-leggity Beasties and Things that go Bump in the night—
     “Good Lord, deliver us!”

The earliest instance that I have found of things that go bump in the night as an independent phrase is from one of the unconnected paragraphs making up the column Notes—Mainly Personal, in the Evening Telegraph and Post (Dundee, Angus, Scotland) of Wednesday 17^th January 1912:

A woman who returned from West Africa gave as the reason not the climate, or the lack of comforts, but “the things that go Bump in the night!”

The phrase has come to be used in the general sense of something that inspires groundless or non-specific fear, as in the following from Gadflights, by ‘Gadfly’, in the Daily Herald (London, England) of Monday 21^st January 1924:

A Tale of Terror

Were your people always Liberals, Henry? If so, what does it feel like? As it happened, mine were not. Had they been, I should have found out what to take for it. A course of trepanning, possibly.
On the whole I’m rather glad that the Fates ordered it otherwise in my case. Because people whose people were always Liberals seem to suffer from the vapours and the fantods and all the other things that go bump in the night. So at least I gather from a typewritten screed which has blown into my operating theatre.
It is in letter form but bears no address and is signed “One who dares not disclose his identity.” Very intriguing, I must say. “Sir,” the letter opens, “My people were always Liberals.” Now you know why he dares not disclose his identity.
But that is not what he is moaning about, really. No, he is concerned to inform me that “the most furious anger is accumulating in the Country” because of the alleged desire of Messrs. Asquith and George to “throw the Empire into the hands of the most frightful gang of Bolshevists the world has ever known.” Yes, superlatives seem to be his long suit, as you remark.
These “gangs” are always minorities, says he. That damned, compact, vermilion minority, as Ibsen might have put it. But they’re very hot, believe me. Or him. By the simple process of dabbling in “underground treachery” and “wholesale trickery” they gain their wicked ends. After that all is plain sailing—or rather, plain slaughtering.
“By brutal terrorism, robbery, rapine and murder,” says my unknown benefactor, “they put out of their way everyone who does not like their ways.” Now could I drink hot blood, so to speak. A sinister lot, whose brains, I am glad to note, are “warped and kinked.” Not to say, soled and heeled.
After a little more concerning the “fiendish eyes” of “the vilest of the vile of the foreign Agitators,” we are informed, calmly and judicially, as it were, that “the trade unions are now but gross frauds.” My friend is not only convinced that the men who are running the trade unions are a lot of bad lads but that they are a lot of ghastly Bolsheviki also. Does he quail? Well, not altogether.
That is to say, although he Dares Not Disclose his Identity, he feels it incumbent upon him to make your flesh creep thick and heavy. “It is the public—YOU and ALL OF US—the Bolshevists want.” Which suggests an almost incredible stupidity on the part of the Bolsheviki, to anyone who knows that amorphous mass, the “public.” But our too-modest friend seems pretty certain about it. “It is YOUR MONEY,” he tells me, “they intend wolfing.” In which case, they can take it from me, here and now, that they’re going to be unlucky!
“One who dares not disclose his identity” (a great pity, with Mr. Gulliver and his fellow-impresarios always on the look-out for new comedians) bids us beware like anything. “Are we and our country to be thus thrown away to a lit of idiots, the tools of a gang of foreign thieves and murderers, to satisfy pique and personal spite,” he asks, omitting the customary question mark in his laudable indignation.
There must be an answer to that. But in vain is the net spread. There’s a catch in it somewhere, and I may as well say I’m not buying it. Not this cruise, anyway.