Quick Answer
A CASPer quartile places your applicant-facing result into one of four broad bands. A 4th quartile result is the highest band, while a 1st quartile result means other applicants in the relevant comparison group generally had stronger responses.
Programs receive CASPer results directly from Acuity Insights, usually about 2-3 weeks after your test. Applicants usually receive their quartile score later, about 4-5 weeks after the test. The quartile is useful context, but it is not the same thing as a detailed numerical score report.
For a broader discussion of competitiveness, read What Is a Good CASPer Score? after this article.