The Ready action allows you to set an observable trigger, and a response to that trigger.
The trigger can be something like, "If the warlock shoots a beam of
eldritch blast at my friend...", and the response could be something like, "...I shoot an arrow at him".
If the warlock has multiple beams, and all beams are simultaneous, then all of the beams will resolve before the arrow is shot, because the response cannot stop the trigger from resolving (unless otherwise specified).
If the warlock has multiple beams, and each beam is shot consecutively, then the first beam (an observable, discrete event) will resolve then trigger the arrow response. If the arrow kills the warlock, then the subsequent beams never get used because there is no live warlock to choose targets.
If the response, instead of being "...I shoot an arrow at him", were "...I
dispel eldritch blast", what happens?
If the beams are simultaneous, then the magic of
eldritch blast has come and gone before the
dispel even starts. There is nothing for the
dispel to target.
But if the beams are consecutive then the first beam resolves, and this triggers the
dispel, which means that the rest of the beams don't get used because the spell itself has gone. If the beams are consecutive then
eldritch blast lasts long enough to shoot every beam. We don't need to know how many seconds it lasts, only that it
must last until the final beam has been shot.
But isn't
eldritch blast an instantaneous spell? Well, it has been argued in this thread that the word 'instantaneous' no longer has any connection to the word in real life! It has been argued that the
only meaning of 'instantaneous' in the game is the *ahem* 'definition' of the word in the Spellcasting chapter of the 5E PHB, on p203 under Duration.
But what does it actually say?
Instantaneous: Many spells are instantaneous. The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant.
Instantaneous spells aren't made of 'magic stuff' that is immune to being dispelled. They cannot be dispelled because the magic has already come and gone before it can be targeted with
dispel magic.
If the beams of
eldritch blast were consecutive then the spell could be dispelled by a readied
dispel magic after the first beam resolves, because the spell
must exist until the final beam is resolved. The rules say that an instantaneous spell like
eldritch blast cannot be dispelled
because its magic exists only for an instant. Therefore, the beams
cannot be consecutive, therefore the beams
must be simultaneous.