When was I conceived?

It gives a window, not a day. Counting back 266 days assumes a pregnancy of average length, and real pregnancies run shorter or longer, so the estimate spans a week either side. It is an estimate from the calendar, not medical advice.

The 266-day count assumes a full-term pregnancy. A baby born early was conceived later than the count says, by about as many days as the birth came before the due date; a baby born late, earlier. Counting back from the due date avoids that: it does not depend on when the baby arrived.

Count back 266 days, 38 weeks. A due date of June 1 points to conception around September 8, and to a last menstrual period around August 25, 280 days before the due date.