The difference between "she explained me" and she explained to me is that when someone wants to describe me to someone while explaining various qualities or feature or overall a general view about object then it is more appropriate to say she explained me.But when I would be in a fix about something while finding the particular thing difficult to understand then if someone comes to help me and tries to explain the thing or to simplify it for me then it would be very much right to say "she explained to me".So in my opinion "she explained me is like portraying a person or to present it to someone for some special reason or may be to present a neutral picture of someone to someone else whom is being misunderstood about the person who is being explained.Sometimes it is difficult to arrange things between two people by themselves and then they need the third party and in such cases it can be used like she explained me.But when a person is unable to clear her /his concept and it can be possible in classroom situation where teachers mostly find themselves explaining various problems to various students.So in both cases explanation is there but about different things but of course information is being provided in both cases.
