How does a company stay operational without profits?

How does a company like instagram,twitter and snapchat keep a staff and stay operational for so long when they don't make money?

There are times when we come across such weird instances where we observe commercial activities being undertaken without the main essence being present, money!
In case of the companies you listed, they are heavily funded due to a niche product they are offering, and limited space for competitors. They are either developing there revenue models or focusing on developing the product further before minting money. Twitter has tried some revenue models like paid/premium tweets, etc. I am not too sure abt the others here. But the money they use is from giant Venture Capitalists who invest in the hope for higher profits. The recent IPO of twitter already highlighted the appreciation of there investments!
So, the core here is, focus on a better product, and make the investors equally confident to ensure funding remains, and once the product is ready, research on the revenue models possible.

Early stage start-up investors speculate on the possible success of an array of companies, lowering their risks by assessing the vision of founders, quality of the teams assembled and clarity of the intended goals. They could be either angel investors (who are more like philanthropists), venture capitalists (who are often companies who make this their business) or even other more established companies.

Typically they make high risk investments in early stage start-ups taking a large percentage of the company in return.

Founders will lay out a plan for a set period of time in which they intend to do x,y, and z, including the relevant hires, will pay £n for this and offer m% of the company to someone with enough cash to invest. The goal of this round of funding will be IPO, acquisition or taking another round of funding from a larger company. A key part of the plan from the founders will be about how they intend to monetise.

So, in the case of a start up with no profit, the money to pay for operations typically comes from an individual or company who makes it's business by making high risk investments.

Often the companies in question don't have high running costs when compared to the amount for which they can potentially sell. If you require $500,000 / year to run in early stages and take an investment round of $1mil for two years, but part with 35% of your company for the money, then your costs are covered and should the investor have a good eye for business and you score a hit with your product, they could be looking at 35% of $1bil in just a few years.