Usually, pets are animals, such as birds or fish that we keep in our homes and take care of. Sometimes, schools will keep "class pets," where all the children take turns caring for this animal. A "teacher's pet," however, is not an animal, but a student in a class who is the favorite of one particular teacher.
Of course, teachers are not supposed to have favorite students, and they should treat everyone equally. Unfortunately, some students try hard to become the "teacher's pet," hoping it will get them better grades. What is even more unfortunate, is that some teachers enjoy the attention those students give, and unconsciously start to favor them. Often, the negative result is that other students resent and dislike the one who is a teacher's pet.