They may perform outsourced government-contracted information gathering or analysis on the down-low -- or "black ops" -- so leaders like Barack Obama can brag that there are officially no American "boots on the ground," as he did with Libya. A leader could say that no CIA agents are in a particular theater while the place is teeming with ex-CIA agents who went private, or even current CIA agents acting in a private capacity in a second job with non-official cover. The media obsession over American war efforts and their negative portrayal has, in part, led to this phenomenon of military support outsourcing. We reap what we sow.
Some work for rich private-investor cowboys looking to make potentially high-risk, high-return investments in the Wild West of emerging markets. They need to know which mobster's or politician's palm they have to grease and who is prone to chopping off hands in lieu of litigation. They may need to vet potential local partners or investors. In these cases, the private spies tap into their network of other current or former spies. It may be ugly, but it's how some countries work. If local embassies openly offered investors such services for a reasonable fee, these private spies would be redundant.
Others spy on multinational companies on behalf of competitors. Capitalism and the principle of free-market fair play get thoroughly corrupted with the outright theft of trade secrets and proprietary information. Espionage for national interest during wartime is patriotic; espionage for strictly financial benefit on behalf of some company against a competitor is grifting. Countries like France are further beefing up laws against such activity, but when uncovered, these cases are usually settled with a financial kiss-off and rarely prosecuted criminally. After all, what federal investigator would want to blow a lucrative post-retirement gig by forcing all the private spying industry's secrets out into the open?