The phrase to recharge one’s batteries and its variants mean to regain one’s energy by resting after a period of exertion.

The image is of restoring an electric charge to a battery.

The earliest use of the phrase recorded by the Oxford English Dictionary (3^rd edition, 2009) is from a letter that the British statesman Winston Churchill (1874-1965) wrote on Wednesday 9^th February 1921 to his wife, Clementine (née Hozier – 1885-1977)—as quoted by their daughter, Mary Soames (née Spencer-Churchill – 1922-2014) in Clementine Churchill (London: Cassell, 1979):

Please my darling think of nothing else but this, subordinate everything in yr life to regathering yr nervous energy, and recharging yr batteries. Don’t throw away yr gains as you make them.

Winston Churchill used a similar image in another letter to his wife:

I do hope you are having fun & tennis & above all recharging yr accumulators.

I have, however, found earlier occurrences of the phrase to recharge one’s batteries—they are as follows, in chronological order:

1-: From Local Brevities, published in the Woodland Daily Democrat (Woodland, California) of Saturday 27^th September 1890:

Colonel Markham, he of the Magnetic hand, arrived on the noon train in company with Harry Morehouse. Markham telegraphed ahead that he would like to have a little rest this afternoon. He will probably use the time in recharging his batteries.

2-: From the St. Johnsbury Caledonian (St. Johnsbury, Vermont) of Thursday 25^th May 1893:

The gospel of rest was promulgated in at least two of the St. Johnsbury churches on a recent Sunday, and the busy men and women of the world received some excellent advice as to the imperative need for an occasional halt in the rush of busines [sic] and society. Just to what extent this advice will be heeded is an open question; but nobody will attempt to deny that the tendency of the present age, especially in America, is altogether too rapid a tendency in one direction, and that the gospel of rest has altogether too few disciples. When men learn just how to let themselves down completely and allow nature to recharge its batteries against future need, better work will be done, with less wear and tear on the human machine, which some people seem to think can, like Tennyson’s brook, go on forever. *

* This is a reference to the following lines from The Brook (1886), by the English poet Alfred Tennyson (1809-1892):

For men may come and men may go,
But I go on forever.

3-: From The Saint Paul Globe (Saint Paul, Minnesota) of Tuesday 1^st December 1896:

The Brotherhood of St. Andrews, Local Assembly No. 32, observed St. Andrew’s day yesterday in its annual meeting and religious services at Christ church.
[…]
Bishop Gilbert, in opening his sermon, said the meeting had been one of the most uplifting of his experience. He believed the brotherhood had been elevated upon a higher plane, and that it would never sink below the level it had gained. It had been a rejuvenation, a recharging of the battery of brotherly love. God, he said, had stored up in the hearts of men, great reservoirs of sympathy, and it needed only the rolling away of the stones from the doors to electrify humanity with the flood of love and tenderness which would rush out.

4-: From an article about the Cornish boxer Robert Fitzsimmons (1863-1917), who was preparing for his upcoming fight against the U.S. boxer James Corbett (1866-1933)—article published in The Boston Daily Globe (Boston, Massachusetts) of Sunday 7^th March 1897:

His friends in the east need have no fear but what he will be right when the time comes. He is down as fine now as he will be, but he will continue hard work until three days before the battle, when he will let up enough to recharge his vitality batteries for the crucial day.