Basically, the Opener is a certain amount of time where you use the skills and buffs you have in a certain manner that can't be upkept for the entire fight (often combined with potions as well).
It tends to deal a huge amount of dmg (more than it would if you spread out selfbuffs and the like over the course of the fight) and therefore increases your overall dps.

For example on BLM, during the opener I have a full timer on Enochian, the buff that allows me to use my main dmg spell (which gets shorter and shorter after each refreshment during the rest of the fight), so of course that gets paired with spellspeed+ and dmg+ and a pot and MP regen so I can throw a crazy amount of superpowered Fire 4's in a short amount of time. After that I have to switch back into a normal-powered cycle of dealing dmg and regenerating MP + refreshing Enochian (the last 2 ones not exactly great for dishing out dmg ). So no, the opener rotation can't be upkept throughout the entire fight.

How much dmg exactly you'll lose nobody can tell you, it depends on how much dps you normally do in the first place, how well you can pull off your opener (there are different ones for different playstyles/level of play), and so on.
You can parse yourself or use SSS to measure the difference though to see how well you fare with and without an opener
But it IS a significant chunk.