Mezzanine financing is just what it sounds like.  It is mid-tier financing, i.e., it is subordinated to senior secured debt but has priority over common equity.  That means that, if the company were to liquidate or file for bankruptcy, the senior secured debt would be paid in full first, then the mezzanine debt, then the common equity.  Mezzanine financing most often takes the form of subordinated notes or preferred stock, often accompanied by warrants with a nominal exercise price.

Mezzanine financing is generally considered to be expensive money.  It's typically designed to provide the investor a higher rate of return in exchange for taking on the risk of being subordinated to the senior debt and usually being unsecured.  Mezzanine rates these day are in the vicinity of 12 percent or more, not counting any additional value added by warrants and other payments.