From Muppet Wiki

The Lecture Lady is an animated character who appears regularly on the "Elmo's World" segments of Sesame Street. The character appears on Elmo's TV, supplying a lecture on whatever the day's topic is. Her actual name/title varies according to the topic, i.e. "The Bird Lady," "The Bike Lady," etc.

In her earliest appearances, the character resembled voice actress Andrea Martin's Edith Prickley character from SCTV. The lecture lady was later redesigned, with longer hair and a rounder, friendlier face.