Resistors:
Resistors are devices that obey Ohm’s law: if there is a voltage drop V across a resistor, then a current I flows from the higher voltage to the lower voltage, and I = V/R, where R is the resistance of the device. So a resistor converts a voltage to a current. A larger resistance produces a smaller current, so a resistor can be used to limit current. Two resistors connected together can form a voltage divider whose function is to take one voltage and produce another, proportionally smaller voltage from it. A resistor connected to a positive voltage (or to ground) can set a voltage at a point where otherwise the voltage would be indeterminate; this is called a pullup (or pulldown, respectively) resistor.
The unit of resistance is ohms, whose symbol is Ω. Since this is hard to type sometimes people use R instead, or SI prefixes such as k or M alone; “1000 Ω”, “1000R”, and “1k” all refer to the same resistance value.
Besides resistance, there are two important parameters for resistors: Power rating and tolerance. The former indicates how much power the resistor can dissipate (current through a resistor produces heat, and too much current will burn out the resistor). For most purposes in synthesizer circuits, 1/4 W is large enough. If not, the BOM should indicate what power to use. Tolerance indicates how close to the nominal resistance the actual resistance may be; 1% tolerance, for instance, means a nominally 100R resistor might be as low as 99R or as high as 101R. Usually 5% tolerance is adequate but sometimes higher precision (smaller tolerance) is needed, and 1% resistors are cheap enough that it makes sense to use them everywhere unless even higher precision is called for.
There are different materials used in making resistors including carbon, carbon film, and metal film. Most 1% resistors are metal film. There are different physical sizes, which generally have to do with the material and power rating, not the value of the resistance.
Here are some resistors:
The value of the resistance and the tolerance are indicated by the colored bands but you may find it easier to just measure the value with a multimeter.
Two different symbols are commonly used for resistors in schematic diagrams:
A potentiometer is a variable resistor.