In Jesus' day there were various schools of thought as to the proper interpretation of Scripture (just as there are today). One rabbi might say that X is acceptable, while Y is not, whereas another rabbi across town might say just the opposite.
Different rabbis had different sets of rules, which were really different lists of what they forbade and what they permitted. A rabbi's set of rules and lists, which was really that rabbi's interpretation of how to live the Torah, was called that rabbi's yoke. ...when you followed that rabbi, you were taking up that rabbi's yoke....
One rabbi even said his yoke was easy.
Rabbis would spend hours discussing with their students what it meant to live out a certain text. If a student made a suggestion about what a certain text meant and the rabbi thought the student had totally missed the point, the rabbi would say, "You have abolished the Torah," which meant that in the rabbi's opinion, the student wasn't anywhere near what God wanted. But if the student got it right, if the rabbi thought the student had grasped God's intention in the text, the rabbi would say, "You have fulfilled Torah."