In more detail
Resistors in series add; in parallel the total is 1 / (1/R₁ + 1/R₂ + …), always smaller than the smallest resistor. On a four-band resistor the first two bands are digits, the third is a power-of-ten multiplier and the fourth is tolerance (brown ±1%, gold ±5%, silver ±10%). Standard values follow the E-series: E12 has 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 and 82 in each decade, and E24 doubles that for tighter tolerances. Each resistor also has a power rating, commonly 1/4 W for small through-hole parts.
Why it matters
Resistors set LED currents, bias transistors, form voltage dividers and pull signals up or down. Misreading one band changes the value tenfold, a resistor run above its power rating overheats, and tolerance means a 1 kΩ ±5% part can measure anywhere from 950 to 1,050 Ω.
Example
Brown-black-red-gold: 1, 0, × 100, ±5 % = 1,000 Ω (950 to 1,050 Ω)
Yellow-violet-orange-gold: 4, 7, × 1,000 = 47 kΩ
Series: 100 + 220 + 330 = 650 Ω
Parallel: 1 / (1/100 + 1/220 + 1/330) = 56.9 Ω
Two 100 Ω in parallel = 50 Ω
Common confusion
A resistor is the component; resistance is the property, measured in ohms, that any conductor has. How resistance relates voltage and current is Ohm's law.