These are IOUs issued by the British government in order to meet the shortfall between its revenue (mainly tax) and its expenditure on public services and defence.
They are generally sold at competitive auctions to institutional investors looking for a relatively safe home for funds however they can subsequently be bought by anyone including retail investors. Gilts mostly carry a fixed income return in the form of a coupon and can be freely traded between issue and final redemption by the government. The nearest US equivalent is the Treasury.