"Mod" is short for modification. An e-cigarette "Mod" in its simplest form is a battery tube normally there are 18650/18350/26650 types. Mod is a tube that holds a rechargeable battery (power supply) with a connection to attach an atomizer.
There are two major variations of e-cigarette mods: mechanical mods and variable voltage mods.
Mechanical mod has no electronic switches, regulators or chips, relying solely on mechanical components and the voltage of whatever battery that is used. It's usually more durable, due to the absence of electronic components.
Variable Voltage mod allows user to change the voltage/wattage output of the device to modify the amount and temperature of vapor.
Mods are especially popular with advanced e-cigarette users, because they require a certain level of familiarity with e-cigarette technology.