Remember that luminosity is the total amount of energy produced
in a star and radiated into space in the form of E-M radiation. The
Sun radiates 3.9 x 10 33 ergs/sec. An "erg" is not a joke,
it is a unit of energy
Start with the Sun
It's easy. Measure its (apparent) brightness, measure it's distance, and use the inverse square law.
The sun emits some amount of total energy from its surface every second
(this is the luminosity of the sun). As that energy is
radiated away from the sun, it passes through increasingly larger
spherical areas. Since the total amount of energy passing through each
sphere is the same, the energy per unit area decreases as the square of
the distance (or the square of the radius of the sphere) from the sun.
This is the inverse square law.
The apparent brightness is a measure of photon energy passing through
a square whatever at the distance of the Earth. One way to determine
the total energy release in photons is to multiply the photon energy
per square whatever, times the total area of the sphere with radius
1 AU (remember an astronomical unit is the distance between the Earth
and Sun) in units of square whatevers.
At the Earth's surface we receive:     1,400,000 ergs/square cm/second.
(Note that a normal-sized human emits 100 watts in IR power.
Strangely enough a black horse in a field on a sunny day absorbs around 800 watts = 1 horsepower).
The energy beating down on the roof per second in solar photons is given
by the solar constant times the roof area:
|Roof Area: 100m x 100m = 104 m2 x|| 100 cm2
||= 108 cm2|
|So: 1.4 x 106|| ergs
||  x   108 cm2||= 1.4 x 1014 ergs/sec|
= 14MW (Mega-Watts)
Is this alot? Total campus usage is 3.5 MW.
We have the energy per square cm per second: 1.4 x 106 ergs/cm2/sec
The Surface Area of a sphere with radius R = 1AU is:
|4 R2 = 4 (1.5 x 1010 cm2 ) = 2.8 x 1027 cm 2|
This is the total energy produced by the Sun   (L stands for solar luminosity).
How much energy is this?
It is pretty hard to get a feeling for numbers this large.
At PG&E rates, the price of the Sun's energy would be 1019 $/sec
Q. What is the Solar Luminosity at the distance of Mars (1.5 AU)?
Still the same, 1 solar luminosity. The Martian "solar constant" will be smaller by a factor of 1.5 x 1.5, but added up over the entire surface of the sphere centered on the Sun with radius 1.5AU, the luminosity is the same. Luminosity is an intrinsic property of the Sun.
Q. What is the Solar Luminosity at the surface of the Sun?   Right, it's still 1 solar luminosity.
A REALLY GOOD QUESTION:
How does the Sun manage to produce all that energy and maintain that production for at least 4.5 billions years?
What about the Luminosity of those other stars?
Once we have the distance to any other star, we can combine that with the apparent brightness and the inverse-square law for light dimming to determine the "intrinsic brightness" or luminosity of the star.
We can therefore determine a luminosity for all the stars for which we have trigonometric parallax measurements.
You will find out that there is a pretty big range from 25 L down to 0.00001 L