The obsolete U.S. nautical expression mark twain denotes the two-fathom mark on a sounding-line.

(Twain is an archaic word for two—cf. never the twain shall meet.)

The earliest occurrence of the nautical expression mark twain that I have found is from the following obscure letter, published in The Tickler. By Toby Scratch’em (Philadelphia, Pennsylvania) of Wednesday 15^th March 1809:
—Context: The inauguration of James Madison (1751-1836) as the fourth President of the USA had taken place on Saturday 4^th March 1809:

For the TICKLER.

Mr. Scratch’em,
Being a constant reader of your paper, I take the liberty to communicate to you some facts, which might have escaped your notice, during the memorable parade in Philadelphia, on the 4^th of March, 1809, in honor of the coronation of Emperor MADISON, the First of the Americas. In the place of him it was given to the French emperor, who now is a prisoner to the little corporal. The first thing struck my attention was, that Madison, the now great man of the nation, took Snyder for a pilot, forgetting poor Tommy altogether as a pilot (contrary to what he told congress on that day) because as how he has run the ship he piloted on shore; and in consequence of not knowing how to manage the ship, or direct her course, resigned his branch, before the wardens of the port had an opportunity of taking it away from him. Secondly, Madison’s capt. sung out in the land sailing phrase, take care Snyder you dont [sic] run me foul of one of those damn’d federal snags, for they are dangerous and a great many of them. Dont [sic] offer to dictate to your pilot, says Snyder, or you will loose [sic] your insurance in case of accident, (meaning his next election) don’t you think I know my duty; while the leadsman was singing out by the deep three.
About this time, some person in Spruce near 3d street, called out to the lad in the chains, you give wrong soundings; upon which Snyder bawled out ready about, tacked and stood to the northward, continuing on a 3d street course, nearly north, as the wind would admit, it being about E.N.E. and in the same soundings, deep three, until she struck against Willings’ tree, and was very near being dismantled.
The capt. sung out, throw all aback; the pilot swore it was impossible the ship could touch in deep three, when she only drew 17 feet water abaft. Ah! but says a knowing one, belonging to the navy, who stood by, she draws as much forward: the capt. taking notice of the soundings, (which he did not do before, being particularly engaged with compliments from the wondering women and children at the windows, crying out, Madison has got the art of sailing ships on dry land) immediately told Snyder there was no such mark on the line as mark three. The astonished pilot looking over the side found the true soundings, which was mark twain, & the mighty Madison in the doldrums. As I turned up Walnut from 3d street, I heard vengeance pronounced upon the first federalist they dare attack; not knowing where this gross insult of the Willing tree would end. I went up to the corner of Fifth and Arch-streets, there I saw the capt. of the vanguard, honorably take ample vengeance by staining his sword with the blood of a federal pig, which run [sic] bleeding and squealing until it expired in the sight of the great Madison and her crow [sic], and to their full satisfaction.
A SAILOR.

It was in reference to the nautical expression mark twain that, in 1863 [note 1], the U.S. novelist and humorist Samuel Langhorne Clemens (1835-1910) chose Mark Twain as his pen-name.

The U.S. author Albert Bigelow Paine (1861-1937) gave the following explanations in Mark Twain: A Biography: The Personal and Literary Life of Samuel Langhorne Clemens (New York: Harper & Brothers Publishers, 1912):

He [i.e., Samuel Langhorne Clemens] was not altogether satisfied. His letters, copied and quoted all along the Coast, were unsigned. They were easily identified with one another, but not with a personality. He realized that to build a reputation it was necessary to fasten it to an individuality, a name.
He gave the matter a good deal of thought. He did not consider the use of his own name; the nom de plume was the fashion of the time. He wanted something brief, crisp, definite, unforgettable. He tried over a good many combinations in his mind, but none seemed convincing. Just then—this was early in 1863—news came to him that the old pilot he had wounded by his satire, Isaiah Sellers [note 2], was dead. At once the pen-name of Captain Sellers recurred to him. That was it; that was the sort of name he wanted. It was not trivial; it had all the qualities—Sellers would never need it again. Clemens decided he would give it a new meaning and new association in this far-away land. He went up to Virginia City.
“Joe,” he said, to Goodman, “I want to sign my articles. I want to be identified to a wider audience.”
“All right, Sam. What name do you want to use—‘Josh’?”
“No, I want to sign them ‘Mark Twain.’ It is an old river term, a leads-man’s call, signifying two fathoms—twelve feet. It has a richness about it; it was always a pleasant sound for a pilot to hear on a dark night; it meant safe water.”

Notes:

1 In his biography of Mark Twain, Albert Bigelow Paine wrote that Samuel Langhorne Clemens’s pen-name Mark Twain “was first signed to a Carson letter bearing date of February 2, 1863”.

2 In his biography of Mark Twain, Albert Bigelow Paine also wrote the following about the pen-name Mark Twain:

That terse, positive, peremptory, dynamic pen-name was first used by an old pilot named Isaiah Sellers—a sort of “oldest inhabitant” of the river, who made the other pilots weary with the scope and antiquity of his reminiscent knowledge. He contributed paragraphs of general information and Nestorian opinions to the New Orleans Picayune, and signed them “Mark Twain.” They were quaintly egotistical in tone, usually beginning “My opinion for the benefit of the citizens of New Orleans,” and reciting incidents and comparisons dating as far back as 1811.
Captain Sellers naturally was regarded as fair game by the young pilots, who amused themselves by imitating his manner and general attitude of speech. But Clemens went further; he wrote at considerable length a broadly burlesque imitation signed “Sergeant Fathom,” with an introduction which referred to the said Fathom as “one of the oldest cub pilots on the river.” The letter that followed related a perfectly impossible trip, supposed to have been made in 1763 by the steamer “the old first Jubilee” with a “Chinese captain and a Choctaw crew.” It is a gem of its kind, and will bear reprint in full today.
The burlesque delighted Bart Bowen, who was Clemens’s pilot partner on the Edward J. Gay at the time. He insisted on showing it to others and finally upon printing it. Clemens was reluctant, but consented. It appeared in the True Delta (May 8 or 9, 1859), and was widely and boisterously enjoyed.
It broke Captain Sellers’s literary heart. He never contributed another paragraph. Mark Twain always regretted the whole matter deeply, and his own revival of the name was a sort of tribute to the old man he had thoughtlessly wounded. If Captain Sellers has knowledge of material matters now, he is probably satisfied; for these things brought to him, and to the name he had chosen, what he could never himself have achieved—immortality.