Pregnancy is supposed to last 39-40 weeks. That means the second trimester ends at 26 weeks. A few states allow elective abortions up to 28 weeks which is in the third trimester. Elective late term abortions has no technical clinical definition, but generally refers to abortions of healthy babies that are viable.
Many states allow abortions up until the baby is deemed viable. Pediatric and obstetrical societies agree viability starts at around 22 weeks. But many of these same states have not updated their "viability" date to at least 22 weeks and so technically they are allowing "late term abortions".
The most common loophole used for late term abortions is depression of the mother (I am not suggesting that some of the mothers do suffer from clinical depression, but it is pretty hard to clinically define the term and the truth is depression can be treated independent of an abortion).
In fairness, late term elective abortions are rare. But rare, is not "none". A survey done of women who had abortions past viabiity indicated the reasons were...
Only about one percent of second- and third-trimester abortions are performed for fetal anomalies, or eugenics
One-third (31%) of the women surveyed said that they misjudged how far along they were
One-fourth (27%) said that they found it hard to arrange an earlier abortion
14% said that they were afraid to tell their parents or their “partner”
The rest gave reasons such as taking their time to decide or waiting for a change in their relationship.
As an aside, I do not oppose late term abortions for mothers that are at medical risk, when an early delivery is not an option.