What a percentile actually measures
A percentile ranks your score against a group of other people's scores. If your score is at the 70th percentile, that means roughly 70 percent of the reference group scored at or below you, and roughly 30 percent scored higher. It is a statement about your position relative to other test takers, not a statement about how many questions you answered correctly.
This is different from a percent score on a normal test, where 70 percent usually means you got 70 percent of the points. An SAT percentile of 70 and a raw score of 70 percent correct are unrelated numbers that happen to look similar.
Why the same score can show different percentiles
College Board publishes percentile tables built from more than one reference group. One common comparison is against a nationally representative sample of students in a given grade, whether or not they actually took the SAT. Another is against the group of students who actually sat for the SAT that year, sometimes called the SAT user percentile. Because these are different populations, the same score can land at a different percentile depending on which table you are reading.
When you look up a percentile, check which reference group the table is using before comparing it to a number you saw somewhere else. Two people quoting different percentiles for the same score are often not disagreeing, they are reading different tables.
Percentiles change every year
Percentile tables are rebuilt from each year's actual test taking population, so a percentile that was accurate for one year's scores is not guaranteed to be accurate for another year's. This matters more the further back the source is. A blog post or forum comment from a few years ago may be quoting a table that no longer applies.
College Board publishes updated official percentile tables, and that is the source to check for a current number rather than a fixed figure repeated from an older source.
Section percentiles versus total score percentiles
Your Reading and Writing score, your Math score, and your total score each have their own percentile, and they do not have to match. It is possible to be at a high percentile in one section and a noticeably lower percentile in the other, and total score percentile is not simply an average of the two section percentiles because of how the underlying distributions differ.
If you are trying to understand your own results, look at the percentile listed for each section on your official score report rather than assuming the total score percentile applies evenly across both.
What a percentile is not useful for
A percentile does not tell you whether your score is good enough for a specific college. Admitted student ranges at individual schools are their own separate number, published in each college's Common Data Set or class profile, and they reflect that school's particular applicant pool rather than the national or user population a percentile table is built from.
Use a percentile to understand how your score compares to test takers broadly. Use a college's own published range to understand how your score compares for that specific application.