MLP stands for master limited partnership. Investors who buy into one are limited partners, rather than shareholders, and have their taxable income reported on K-1s, rather than 1099s.
MLPs are engaged in businesses (e.g. real estate, natural resources) that generate a lot of cash that doesn't need to be "reinvested," or put back into the company.
Because of this feature, the IRS will exempt it from corporate tax if it pays out at least 95% of its income in the form of dividends. The advantage is that you avoid the "double taxation" common to most corporations, and get a higher yield as a result.
The disadvantage is that the company can't retain earnings for growth, and needs to borrow money if it wants to grow. In this regard, an MLP is much like a utility (except that a utility has to pay corporate taxes, and is otherwise heavily regulated by the Federal and/or state governments). You can look upon an MLP as an unregulated utility.
This means that MLPs are most suitable for utility type investors who are more interested in current income, than capital gains. Because they are unregulated, they are riskier than utilities.