This is worded a bit confusingly but it's important to note that the extra target ability is provided as an option in the Accelerate text.
Accelerate (4+ Intellect points): (...) In addition to the normal options
for using Effort, you can choose to use Effort
to affect more targets; each level of Effort
affects one additional target. You must speak to
additional targets to accelerate them, one target
per round. Action per target to initiate.
It saves you having to spend the initial high intelligence cost again and again.
For example, without effort, to cast on three targets it would cost:
Base 4 + Effort(1st) 3 + Effort(2nd) 2 = total 9 int
To cast this ability for up to 3 targets essentially giving you three charges to give out. Then spending the next three turns using up those charges by talking to the targets one by one.
Alternatively you could activate accelerate every turn but this would then cost the speaker an additional 3 int points:
Base 4 + Base 4 + Base 4 = total 12 int
Edge complicates these totals potentially reducing the total Base + efforts used. The first option is simply cheaper if you know you are going to use it without edge.
But it also makes more sense if you have a few rounds to prepare for the approaching abhuman horde!
For particularly skilled Speakers though with an intelligence edge the second option will be better though especially later on in a campaign. But at low tiers it might still be useful to consider using it when you don't have the time to stop and give a few encouraging words to your allies. A quick 1 action buff for 1 target might make all the difference.
Since the revised cypher system core rulebook was published it has been possible to obtain this ability as a mid tier focus ability on any character type potentially one without any intelligence edge making the first option highly viable to those users. The mid tier support foci option lists can be found on Page.105 of the revised core rulebook.