When you explain something to someone, you provide information. Sometimes that information is detailed steps on how to do something.
Sometimes a teacher typically wants to provide just a little direction to students and then have them learn on their own, the idea being they will understand things more strongly if they have done most of the work themselves.
Sometimes the student is having trouble and tells the teacher, "I'd like you to explain this", asking the teacher to provide detailed steps.
Teach works like give and takes two objects.
I'm going to teach you the proper way to do this.
So there could be temptation to use explain in the same way.
Can you teach me the steps?
Can you explain me the steps in the more detail?
However explain doesn't really work like teach.
The origin of the word explain (reference) provides some clues:
early 15c., explanen, "make (something) clear in the mind, to make
intelligible," from Latin explanare "to explain, make clear, make
plain," literally "make level, flatten," from ex "out" (see ex-) +
planus "flat" (from PIE root *pele- (2) "flat; to spread").
Basically, when you explain something, you're "laying it out flat so it's more easily seen/understood". The model here is that you are doing something to the thing you are explaining to make it more understood. The person needing the explanation should be "taking" it.
though the teacher explains to her repeatedly.
This sounds awkward because the reader/listener doesn't know what is being explained./
Unless context is strong enough for the reader/listener to automatically fill something in, the one required object of explain needs to be expressed.
Allow me to explain.
Explain here is an infinitive and those don't always need objects. Also, if you are literally asking someone to allow you to explain something, that's a pretty strong context and they will know what you are trying to explain to them.