The British Army was very different in the 18th century to how it is now. Our modern system is based on the Cardwell Reforms that occurred between 1868 and 1874, which mandated military training for all commissioned officers, and abolished commission buying, amongst other things.
Commission buying is the act of purchasing a 'commission': as in, purchasing the commission from the crown to serve as X rank in Y regiment. These were considered personal property and could be traded and sold almost at will. Reforms introduced by Frederick William, the Duke of York and son of George III, in the late 18th century meant that ranks carried a requirement of time served in the preceding rank. However, for a large portion of the British Army's history, it was technically possible to buy up to the rank of Full Colonel in the British Army. Above that is the general ranks, which can only be given out on special appointment by the sovereign.
John Moore, the Duke of Wellington, Ralph Abercromby, Rowland Hill, Robert Craufurd, Thomas Picton, were all benefactors of this scheme. It had various drawbacks, though some advantages was that it encouraged what were considered the 'top echelon' of society to participate in the armed forces. and eased their transition to an appropriate rank. It also meant that it was possible for private individuals to raise, finance, and supply regiments for the country, then buy the commission to command their own regiment.
The drawbacks were obvious. Officers with little to no professional training, the view of the commission as personal property made cashiering a huge step that was rarely taken, various corruption, the stratification of the military in the hands of the very rich, officers not actually serving at all and just living off half-pay from their rank. However, for the purposes of the Georgian army, it suited well enough.