I would assume it's a startup that complies with regional non-profit rules. For example, in the USA, there's the 501(c) non-profit designation that has explicit rules set by the government, mostly for tax purposes.
Often, if your company complies with these rules, you don't pay as much in taxes (often nothing). Usually non-profits set out to improve the world, in what ever way they see that the world needs improvement (not everyone has to agree that they are, in fact, improving the world).
First, draw a dividing line between being a nonprofit (which is a function of being formed as such under state law) and being a public charity (aka a 501(c) organization) which is a function of being a nonproft under state law AND submitting a Form 1023 to IRS. Second, there are many new social ventures which take on varying formats - not for profit corporations, benefit corporations, low profit limited liability companies, joint ventures and ownership of for profit entities, etc. The startup mentality - agility, speed to market, customer focus, energy, etc. - are all equally as present in these entities as in for-profit startups.