Rest on one's laurels
To be satisfied with one's past success and to consider further effort unnecessary.
The laurels that are being referred to when someone is said to 'rest on his laurels' are the aromatically scented Laurus Nobilis trees or, more specifically, their leaves. The trees are known colloquially as Sweet Bay and are commonly grown as culinary or ornamental plants.
The origins of the phrase lie in ancient Greece, where laurel wreaths were symbols of victory and status. Of course, ancient Greece is where history and mythology were frequently mixed, so we need to tread carefully. The pre-Christian Greeks associated their god Apollo with laurel - that much is historical fact, as this image of Apollo wearing a laurel wreath on a 2nd century BC coin indicates. The reason for that association takes us into the myth of Apollo's love for the nymph Daphne, who turned into a Bay tree just as Apollo approached her (anything could happen if you were a Greek god). Undeterred, Apollo embraced the tree, cut off a branch to wear as a wreath and declared the plant sacred. Their belief in the myth caused the Greeks to present laurel wreaths to winners in the Pythian Games, which were held at Delphi in honour of Apollo every four years from the 6th century BC.
Following the decline of the Greek and Roman empires, the use of wreaths of laurel as emblems of victory seems to have taken a long holiday and didn't re-emerge until the Middle Ages. Geoffrey Chaucer referred to laurels in that context in The Knight's Tale, circa 1385:
With laurer corouned as a conquerour
And there he lyueth in ioye and in honour .
[With laurel crowned as conqueror
There he lived in joy and honour]
A 'laureate' was originally a person crowned with a laurel wreath. We continue to call those who are especially honoured laureates although the laurel leaves are usually kept for the kitchen these days. Nevertheless, laureates benefit in other ways; Nobel Laureates get a nice medal and 10 million Swedish Krona and Poets Laureate (in the UK at least) get a useful salary and a butt of sack (barrel of sherry).
As to the phrase's meaning, to 'rest on one's laurels' isn't considered at all a praiseworthy strategy - it suggests a decline into laziness and lack of application. That's not the original meaning. When 'rest on one's laurels' or, as it was initially, 'repose on one's laurels' was coined it was invariably part of a valedictory speech for some old soldier or retiring official. An early example of that usage is found in The Memoirs of the Cardinal de Retz, 1723:
The Duke [of Orleans] was old enough to take his Repose under the Shadow of his Laurels.
Of course, the 'repose' was figurative - no one was imagining someone sleeping on a bed of laurel leaves, although the citation above could be construed as referring to laurel trees rather than laurel wreaths. No such doubts with a slightly later citation from the London-based Gentleman's Magazine, 1733, on the retirement of a schoolmaster of Westminster School:
So thou, paternal Sage, may'st now repose.
Nor seek new Laurels to adorn thy Brows.
As soon as we move into the energetic 19th century, the meaning changes and the phrase is used with a distinctly disapproving tone. The review magazine The Literary Chronicle, 1825, which praises the work of Maria Edgeworth:
We do not affect to wish she should repose on her laurels and rest satisfied; on the contrary, we believe that genius is inexhaustible... For Miss Edgeworth there must be no rest on this side the grave.
We are hardly any more charitable these days. 'One-hit wonders' are sneered at and, with proper Anglo-Saxon earnestness, Anthony Burgess dismissed his fellow author Joseph Heller's inability to write a second book for 13 years following the success of Catch-22 by sniping that "Heller suffers from that fashionable American disease, writer's block".