verb forms - Why do people say "explain to me", not "explain me"?

Is there any grammatical rule to know which verbs can (or better, must) be sometimes followed by "to"? Some examples are:

• Please explain to me why...


• She said to me that...

I'm aware I could also say "explain me", but such thing would mean something like "explain what I am" or "give an explanation of myself". However, you could never use "say me". In other cases, it seems both formats are acceptable. An example would be:

• "Show me" and "show it to me"

Is there any rule to explain this?