The phrase the best, or the greatest, etc., thing since sliced bread is an expression of enthusiastic appreciation, especially of a new invention or discovery.

The earliest mention of ready-sliced bread put up on the market that I have found is from The Constitution-Tribune (Chillicothe, Missouri) of Friday 6^th July 1928:

Announcement by M. F. Bench of the Chillicothe Baking Company of a new sliced bread service is significant in that it gives the Chillicothe Baking Company the distinction of being the first bakers in the world to sell sliced bread to the public.

Later improvements in the baking industry were often assessed by comparison with the introduction of sliced bread. For example, the following advertisement for Walsh Baking Company’s Golden Toast Thick and Thin was published in The Evansville Press (Evansville, Indiana) of Friday 22^nd December 1933:

The Toast of the Whole Town…

[…]
Don’t be fooled. There’s only one Golden Toast. The careful blending of ingredients, the skill in baking, they haven’t changed one iota. We’ve merely added the first improvement since sliced bread . . . thick and thin slices in the same loaf.

Likewise, the following is from The Tampa Daily Times (Tampa, Florida) of Monday 12^th November 1934:

Dated bread, guaranteeing that it will reach the housewife in fresh condition, has been put on the market here by Bell Bakeries. The management announced that the company’s new Bell Vitamin B white loaf with green and red wrapper will be plainly dated for freshness.
“This is the most progressive step that has been taken in the baking industry since sliced bread was introduced,” said N. R. Farrar, general manager of Bell bakeries.

The following advertisement was published in the Lafayette Journal and Courier (Lafayette, Indiana) of Saturday 29^th July 1939:

HAVE YOU TRIED
RUGER’S
NEW
Pantry-Package
TWIN STYLE
White Bread
?
IT IS THE
NEWEST THING
Since
SLICED BREAD
●
On sale at your
grocers.

Therefore, the phrase the best, or the greatest, etc., thing since sliced bread is a kind of spoof marketing slogan. The earliest instance that I have found is from The Northern Whig (Belfast, Ireland) of Thursday 8^th March 1951, which quoted the American journalist Dorothy Kilgallen (1913-65) writing in the New York Journal-American:

Stewart Granger* “is the greatest thing since sliced bread”

Stewart Granger is the latest “heart-throb” in the United States.
Miss Dorothy Kilgallen, writing the New York “Journal-American,” said this of Granger, who recently married Jean Simmons and is now working in Hollywood:—
“Judging from the reactions of some of my normally sane female friends to a recent film called “King Solomon’s Mines,” I have come to the conclusion that the motion picture moguls don’t realize what they have on their hands in the person of Stewart Granger.”
[…]
Miss Kilgallen quoted “one damsel” as saying: “He’s so divine, every time he came on the screen I felt sick in my stomach.”
And another: “I’ve dreamt of him every night since I saw the picture six weeks ago.”
And a third (Miss Kilgallen’s own sister): “He is the greatest thing since sliced bread!”

* Stewart Granger (born James Lablache Stewart – 1913-93), English actor