In effect, luminosity is the measure of a star's brightness; the greater the greater the luminosity the brighter the star appears.
Put another way, the luminosity is the measure of how much energy per unit time the star is releasing (i.e. the rate of energy release). This energy is mostly emitted as electromagnetic radiation (light), however other forms of energy, like neutrino emission, is included as well.
In most cases, luminosity is meant to relate how much energy in the form of light is being emitted by an object. However, the luminosity can also depend on the wavelength of light emitted.
For instance, neutron stars are typically very bright in the X-ray and Radio bands (though not always; some are brightest in gamma-rays), so these objects could be said to have high X-ray and Radio luminosities, but have very low optical luminosities.
It is not common for publications to mean the integrated luminosity, that is the total luminosity over all wavelengths, when the term luminosity is used. This is because individual band luminosities are usually stated as such.
In astronomy luminosity is often times expressed in terms of solar luminosity; that is, the luminosity of the sun, usually expressed L๏.
For instance a star that has triple the luminosity of the Sun would be expressed to have a luminosity of 3 L๏.