Why do we add "a" in some sentences?

Why do we add "a" in some sentences?
 

HI everyone,

I got a problem recently. I found in many places that though the English translation clearly does not require the "a", the spanish sentence usually has an "a" in certain places. For example:

La madre culpa a su hijo.
Yo motivo a mis alumnos.
Ella mantiene a su hijo.

Could you guys share some of your thoughts on that? Thanks :)

I find this use of a really annoying, but it's quite common. A has many uses, and you would expect it only to introduce an indirect object, as in

Mateo dio un beso a su madre

But the a you are asking about is the 'personal a' which relates the subject to a personal and known direct object

Vi ayer a Juan

As an example, you would use a for animals kept as pets, but not for animals in general.

¡Ven a ver a mi cachorrito!
El gato cogió el gorrión

That's a very general statement for a start, I bet there is a thread on it here somewhere. :)

Thanks very much Perikles and the website above, these are very detailed explanations and I got your points :)

Here is another concern about it. As for the usage of "personal A", can this "a" be emitted in some cases or it is required whenever the direct object is a person or person-alike?

No it can't be omitted in that case. If you do the meaning will change.

Thanks a lot~!