The term modification has been applied to e-cigarettes since long before vaping was mainstream (not that it is mainstream in many countries even now, hopefully you get my meaning though). These days modification or mod for short has come to mean ‘anything not an ego/pen/cigalike’. To read more about that version, see the entry for mod as that’s the most common word used these days.
Now, back to the good old days… Before modern mass produced ‘mods’ existed, if you wanted something with a larger battery, better flavor, or more of anything really you would have to make it yourself. To simplify this, people turned to the most commonly available item which used large enough batteries that could also output enough power to vape “safely”. This meant torches (or flashlights), or torch modifications as they became known, shortened to modification and then mod. Many torches actually use the very same batteries we use to vape (18650’s). So modifying a torch to include a 510 thread and connector you could screw on an atomizer base and fit an atomizer head and cartridge to it and vape with a bigger battery.
Not long after this, people worked out you could get rid of the cartridge by attaching a drip tip directly to the atomizer cone (which happened to be the size we now know as a standard 510 drip tip). This setup was effectively the first dripper on the first mech mod.