Social Security Has Three Ages That Matter: 62, 67 and 70
Direct answer
If you were born in 1960 or later:
62 = the earliest you can start. It comes with the lowest benefit.
67 = your full retirement age. It comes with your standard benefit amount.
70 = the age when you get the maximum benefit from waiting. Waiting longer will not increase it further just because you delayed.
But those are milestones, not the only ages when your benefit changes.
Your Social Security amount changes month by month between 62 and 70.
Updated

The three ages
62 = earliest and lowest
67 = full retirement age and standard amount
70 = maximum from waiting
Your benefit changes every month
You do not have to choose only 62, 67 or 70.
You can start in any eligible month between 62 and 70.
The longer you wait, the higher the monthly benefit becomes, all the way up to age 70.
No one told me the benefit keeps increasing every month
A lot of people assume there are only three benefit amounts:
a small one at 62
a standard one at 67
a big one at 70
That is not how it works.
Think of 62, 67 and 70 as milestones on a sliding scale.
Simple example
Suppose your full-retirement-age benefit at 67 is $3,000 a month.
For someone born in 1960 or later:
At 62:
about $2,100
At 62 + 1 month:
about $2,112
At 67:
$3,000
At 67 + 1 month:
about $3,021
At 68:
about $3,240
At 69:
about $3,480
At 70:
about $3,720
The exact dollar amount depends on your own Social Security record.
The point is the pattern.
What happens between 62 and 67?
Each month you wait makes the early-claim reduction smaller.
What happens after 67?
Delayed retirement credits increase the benefit by about 8% per year, or 2/3 of 1% per month, until age 70.
And what about age 65?
Age 65 matters primarily because of Medicare.
For most Gen Xers:
Medicare age = around 65
Social Security full retirement age = 67
Those are different clocks.
The bottom line
62 = earliest and lowest
67 = standard amount
70 = maximum from waiting
The three ages are milestones, not three price points.
Your Social Security benefit keeps changing month by month between 62 and 70.