Pay for a purchase.
This phrase derives from horse trading or other dealing where money was put onto a wooden post (stump) to display good faith in a cash deal. It is a variant of the expression 'cash on the nail'.
The Reverend William Carr published a glossary of the colloquial language of the Craven district of West Yorkshire in 1828, titled The Dialect of Craven, in which he defined 'stump' as a verb:
"Stump, to pay ready money,... to pay down on the nail."