Two circuits on right show the equivalence of resistors in series. Two circuits on left show the equivalence of resistors in parallel.
Top left circuit is two resistors in parallel, R1 and R2. The equivalent resistance, Rp, is in the bottom left circuit. The resistors in parallel equation is Rp = (1/R1 + 1/R2)^(-1). In this example: (1/1000 + 1/1000)^(-1) = 500.
Top right circuit is two resistors in series, R1 and R2. The equivalent resistance, Rs, is in the bottom right circuit. The resistor in series equation is Rs = R1 + R2. In this example: 1000 + 1000 = 2000.