LED's with switch on a 12v supply
Series circuit







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Five LEDs in series.

LEDs aren't linear (current is not proportional to voltage as in a resistor) and small increases in voltage can cause a large increase in current to the point of destruction. A series resistor will limit the current to a safe value provided voltage doesn't deviate too much.

Since you require 2 V per LED at 10 mA that means we need to drop another 2 V in the series resistor. From Ohm's Law, \$ V = IR \$, we can calculate \$ R = \frac {V}{I} = \frac {2}{0.01} = 200~\Omega \$. 220 Ω is the next highest standard value.

Parallel connection







simulate this circuit

Figure 2. Parallel circuit.

This time each LED requires its own resistor which needs to drop 10 V across it. Using Ohm's Law again we get \$ R = \frac {V}{I} = \frac {10}{0.01} = 1000~\Omega = 1~k\Omega \$.