A logic analyzer is an electronic instrument which visualizes a set of digital signal across time. It can only display logic levels and their transitions, not analog levels.
Logic analyzers often include extra features like triggers and signal/protocol analyzers:
A trigger will make the analyzer wait with capture until a certain condition is met, typically a rising or falling edge. More advanced logic analyzers often has more advanced trigger configurations.
A signal/protocol analyzer will look at one or more signals at a time and display their values. Many logic analyzers have support for asynchronous serial lines, I2C and SPI while the more advanced ones have support for more protocols.
For more information see Wikipedia.
