The words “Platform as a Service” should be enough to send any sentient being to sleep. But, people of the drowse, they are important ones, not least because between the four of them they account for a lot of enterprise spending.

That’s why companies like Apprenda can exist in upstate New York and raise two rounds of funding totalling $15 million without anyone really knowing who they are.

Today, Apprenda is rolling out version 4.0 of its flagship platform, which it reckons melds the best of the public and the private cloud to serve big companies that are trying to haul themselves into the new “as a service” world, while holding on to the formal structures of app development, maintenance, and security that have served them well until now.

Just to make it clear: PaaS is a layer of technology on which developers can build, maintain, and monitor applications, all delivered in a simple, fill-in-the-blanks format that makes developers’ jobs easier.

With the new version of Apprenda, companies can shift seamlessly between private and public cloud with the click of a button, based on business needs and specific parameters. This hybrid-cloud architecture lets developers build next-generation, cloud-architected apps while updating existing in-house apps with minimal adjustments to the code. That way, businesses get to retain the security of the private cloud with the convenience and scalability of the public cloud.

Many big companies realize that hot enterprise-focused startups, including the likes of Box, Asana, and Atlassian, are making business software cheaper and more flexible than ever before. In the PaaS space, Google, Microsoft, Amazon, and Salesforce all have products in the game, but enterprises with legacy-bound systems and processes are reluctant to drop everything to jump on board the new movement, even if they realize that not doing so might ultimately cost them a competitive advantage in terms of agility and being able to move with the times. Such enterprises have years of private data and tech infrastructure tied up into applications that were previously the domain of in-house tech teams.

Apprenda believes they’re not about to let go of all that in a hurry, and so it licenses its technology to enterprises and has it integrate with their on-premise applications so that they can get used to consuming cloud-based platforms without giving up control of the platforms they already trust and have invested in.

Sinclair Schuller, Apprenda’s founder and CEO, says that while other PaaS companies focus on helping companies deploy apps, that’s not what keeps enterprise developers up at night. “We’ve captured and commoditized architecture patterns,” says Schuller, which basically means that Apprenda lets developers write apps in the language they already know, while being able to integrate with public cloud for mobile and Web-scale apps, if they so choose.

PaaS is the fastest-growing area of cloud computing. Gartner predicts that the worldwide enterprise market for PaaS platforms will grow from $900 million last year to $2.9 billion by 2016, a 26.6 percent year-on-year increase. Apprenda has taken advantage of such forecasts to raise big-money rounds, starting with a $5 million Series A round in 2008, led by NEA, and a $10 million Series B round in 2010, lead by Ignition. The company says a Series C is in its “near future.” It has more than 30 staff, spread between Albany, New York, New York City, and remote locations.

Apprenda’s 4.0 upgrade comes in the midst of a big week for cloud computing. Amazon Web Service’s Re:Invent, its first global customer and partner conference, takes place this week in Las Vegas, as does VentureBeat’s CloudBeat, in Redwood City. Also in Vegas, Gartner is hosting its Application Architecture, Development & Integration Summit, and Citrix is staging its first CloudStack Collaboration Conference.

So if you really don’t like terms like “Platform as a Service,” it might pay to look away for a week or so.