A convertible note is one of several ways to structure an early financing round before a properly priced equity round. Another way is the "safe note".
According to http://seedinvest.com, the definition of a convertible note is as follows:
"A convertible note is a form of short-term debt that converts into equity, typically in conjunction with a future financing round; in effect, the investor would be loaning money to a startup and instead of a return in the form of principal plus interest, the investor would receive equity in the company."
Fred Wilson, an avid blogger and VC at Union Square Partners, has a fantastic and comprehensive blog post on the topic of convertible posts. This post also talks about warrants. (What's a warrant? Read the post to learn more.)