Thévenin's
Theorem is a theorem regarding electrical
circuits. Any linear network with an
open circuit (2 terminals) can be represented and simplified to one smaller network with one voltage source and one single series
resistor. Because it allows electrical engineers to greatly simplify otherwise complex circuits, Thévenin's Theorem is a blessing.
In order to find the resistance that equivalent resistor would have, trace an imaginary current from one terminal to the other, and sum up the resistances according to the laws for resistors in parallel and in series. Here's an example of finding the Thévenin equivalent resistance and voltage on a simple circuit. Please forgive my terrible ASCII art skills.
1 Ohm resistor
/\/\/\/\O
 
 
/+\ /
/ \ \
 3V 3 Volt / 2 Ohm resistor
\ / voltage \
\/ source 
 
 
O
Let's figure out the Thévenin equivalent resistance. Replace the voltage source with a short circuit, as if the voltage source were not there at all but the network was still completely connected. Trace an imaginary current from one terminal to the other. The resistors are in parallel, so:
1 1 1
 =  + 
R R R
total 1 2
or,
R (R1)(R2)
total = 
R1+R2
So the Thévenin equivalent resistance is 2/3 Ohm. As for the voltage, using a voltage divider produces:
(2 Ohms)
V = (3 V)  = 2V
(1 Ohm) + (2 Ohm)
So, a much simpler equivalent circuit to the one shown above would be:
2/3 Ohm resistor
/\/\/\/\O


/+\
/ \
 2V 2 Volt
\ / voltage
\/ source


O