Green’s Dictionary of Slang

1. an important person.

1884		Life 24 Jan. 48: His honored father was one of the biggest potatoes – as the phrase is [in Boston] [HDAS].
1893		F. Harris ‘Gulmore, the Boss’ in Elder Conklin & Other Stories (1895) 241: It isn’t that the big potatoes want pertic’lar to come to the top, it is that the little potatoes are determined to get to the bottom.
1926		Wood & Goddard Dict. Amer. Sl. 41: potato. A person; as in a big potato, small potates.
1931		Irwin Amer. Tramp and Und. Sl. 28: big spuds.— Any group in authority, such as a Parole Board, Board of Directors, etc.
1934		G. & S. Lorimer Stag Line 167: How did that bunch of gills ever get to be the big spuds in the business world.
1950		Goldin et al. DAUL 162/2: Potato. (Usually in the phrase, ‘a big potato’) A big shot; anyone who has money, influence or the appearance of having either.
1978		W. Diehl Sharky’s Machine 348: This guy’s big potatoes. He’s powerful.
1999		Guardian G2 17 Aug. 22: As Field Marshal Smuts said admiringly to Queen Mary ‘You are the big potato’.

2. a large but stupid man.

1937

T. Thursday ‘The Wild Whampoo of the Whampolo’ in Blue Ribbon Sports Dec. 🌐 ‘I hope the ambulance service is good in this town,’ said Foghorn. ‘Me, too,’ said Montmorency. ‘That big potato over there will need it.’.

3. usu. in pl., an important event.

2022

Byline Times 17 Jan. 🌐 The libel action brought by Arron Banks, the man behind Britain’s biggest political donation [...] against Observer and Guardian journalist Carole Cadwalladr is big potatoes.