Twitter is an interesting business and social network. The service is described as a micro-blogger, that is, it allows users to share what's happening in their life at that particular moment in 140-character chunks. It's been picked up and used by businesses and organizations as a source for daily news and real time, or near-real time updates. However, as Twitter has become a more commercialized space, so the growth in monthly active users has declined. Twitter is trapped between needing to monetize the service and keeping its current users engaged and involved. From a stock market perspective, following Twitter's Initial Public Offering, or IPO, the business has underperformed compared to its competitor social media businesses. Instead, the business has been put into the "business media" shoebox and considered a business that cannot shoot straight and one that is perhaps not really for the intense scrutiny that floated businesses must undergo every quarter. Given the pressure on Twitter, it is perhaps not surprising that there are stories circulating detailing how both Google and Twitter could benefit from one another should Google buy Twitter.
An article in the fool.com website details some of the reasons why Twitter might benefit from the acquisition, including how Twitter's business numbers would be masked by being a part of Google (and this would ease the pressure onto Twitter) and how the stock-based compensation expenses would be more palatable for shareholders (last tax year, Twitter's compensation expenses totaled almost half of the revenue base). Using Google's opaqueness to disguise Twitter's quarterly revenue does not seem a sensible reason to invest. It's true that Google would benefit from a service growing faster than its core business and management may be able to enhance shareholder returns from the Twitter business. The article also mentions that Google has $59 billion in cash, around three times Twitter's current market valuation, and that buying Twitter might be a way to reward Google shareholders.
How well a fit into Google's business would Twitter be? We've seen Twitter expanding their messaging services, which to a point would put them into competition with Google Hangouts. Perhaps Twitter could be used as a business communications tool, but Google has a habit of running an acquired businesses as a standalone project. All the same, it is difficult to imagine Twitter become a Google service: simply finding a home for some of Google's cash deposits is not reason by itself to invest in another business.