A standard cohort consisted of 6 centuries (80 soldiers each plus 20 support staff) - a total of 600 men.
However the first cohort had 5 double sized centuries (160 soldiers each plus 40 support staff each) for a total of 1,000 men.
So why was the first cohort larger than the others?
The size of the First Cohort being inflated was a temporary phenomenon probably after Marian Reforms and undoubtedly in effect during the early Principate but eventually teetered out. Some historians have pointed to archaeological evidence from certain periods from camps that the First Cohorts buildings were identical to all the other Cohorts, indicating that the size expansion was not a permanent feature of the Roman Army.
That being said the most prominent theory amongst academics is that the expanded size was the placement of all specialty soldiers into the First Cohort (support troops basically. The older theory is that the greater size was to protect the Standard that it carried, but this is dubious since only one Century would really have control over it and the Centurys a couple units down would have little to no effect in protecting the Standard in the right confines of battle.