A blue chip is a large and well established company, or its shares. The key criteria is that these are large companies, primarily in terms of market capitalisation. The term also implies financial strength and stability.
Blue chip shares are often regarded as less risky that those of smaller companies, but there are plenty of examples of blue chips performing extremely badly. Investors should rely on diversification and proper assessments to control risks, rather than simply equating blue chip with safe.
It is perfectly possible for large cap stocks to perform badly, as investors in GEC (renamed, first Marconi, and then Telent) discovered: someone buying the share at its peak would have lost almost their entire investment. Investors in large telecoms companies during the dot com boom also made substantial losses during the bust.
The origin of the term appears to lie in gambling, with blue counters in casinos being the most valuable.
While the definition of blue chip is a little vague, it is often used of companies that are constituents of large cap indices such as the the FTSE 100 in the UK or the Dow Jones Industrial Average in the US.