In more detail
Rearranged, the law gives I = V / R and R = V / I. Combined with power, P = V × I, it also gives P = I² × R and P = V² / R, so knowing any two of voltage, current, resistance and power lets you find the other two. It describes resistors and metal conductors at a steady temperature well; diodes, LEDs and lamps do not follow it, and a filament's resistance rises sharply as it heats up.
Why it matters
It is the everyday tool for choosing a Resistor, sizing a fuse or checking whether a wire will run hot. A resistor's power rating matters as much as its value: one that dissipates more than its rating overheats and can fail.
Example
Current-limiting resistor for a red LED (about 2.0 V at 20 mA) on a 9 V battery:
R = (9 − 2.0) V / 0.020 A = 350 Ω → next standard E12 value up: 390 Ω
I = 7.0 V / 390 Ω = 17.9 mA
P = 7.0 V × 0.0179 A = 0.126 W → a 1/4 W resistor is enough
12 volts across 4 ohms drives 3 amps, which dissipates P = V × I = 36 watts.