Something along the lines of: okay so you have this guy who's a criminal right? (expand node) here are his phone numbers (expand node) here are the phone numbers who called it (expand node) here are the phone numbers who called those numbers (expand node) here are who they're registered to (expand node) here are their addresses (expand node) here's who else lives there.
I still assume their special sauce isn't their ability to build a node expanding UI, but the data sources they have access to. If they're used for so many government contracts, they're definitely using the data from, say, one police department to inform another. So when another department wants data about criminals, they sign up as a client for the company where that data already is.
And don't discount that the government would pay a huge sum of money to build a surveillance state, even if that surveillance state turned out to be pretty useless.
Of course the NSA has been doing this for years, but their UI probably isn't as pretty as Palantir's :)
Not long after that, I found out that Palantir got their first energy industry customer. Some employees in Palantir thought it wouldn't be worthwhile to go after oil & gas companies because they viewed them as old school and slow to adapt to new ways of doing things. However, in those days Palantir was focused on acquiring no more than one customer per industry, because they were trying to boost their valuation as quickly as possible and wanted to demonstrate how many industries they could serve. And then, due to a contrarian within the company, they did get an O&G customer, and it was the biggest single deal so far in the company's history.
What I don't know is exactly how well they served that customer. What I do know is that they were selling the customer on the idea that they have sooooo much data and they're leaving tons of low-hanging fruit that could easily boost savings in the company. Stick all this data into Palantir's product and we'll help you on a million fronts and therefore boost your profits significantly. One example is the longevity of machine parts and all the data you can get about historical wear and tear, etc. Now, this is what they were selling, and I don't know which areas ended up being the most helpful, but yeah, as someone else in here said, they were insisting on customers putting in all the data they have and the product would make connections, or reveal insights, etc.
Even if it's a crude product by Star Trek standards, you've gotta admit there is probably a ton of low-hanging fruit like that in most companies, and a lot of the time they don't go after all that because they're making money, but just don't have extra manpower or expertise to look into all that, so if Palantir delivers on the promise to boost the bottom line, then I guess it's worth it. It also means there's room to compete, although a big problem is even if you're a sharp cookie, Palantir probably started with way more business connections than most nerds will ever have.