All of them mean different things. It's just in English they are translated with the same word.

"здесь" indicates a location, and answers the question "где?" (where?):
Я здесь. - I am here. Мой друг живёт здесь. - My friend lives here. Мы здесь работаем. - We work here (in this place). Здесь много людей. - There are many people here.

"сюда" indicates a direction, and answers the question "куда?" (to where?):
Он идёт сюда. - He is walking here (to this place). Я приехал сюда 3 года назад. - I came here (to this place) 3 years ago. Сюда приближается торнадо. - A tornado is approaching here.

"вот" is a completely different word. It is not even an adverb (unlike "здесь" и "сюда"), it is just a particle which we use to show something. (An indicative particle).

It roughly corresponds to English constructions like "Here is A" or "Here it is".

You invite your friend to your home and show him your room: "Вот моя комната" (Here is my room).
You show me a book and say: "Вот книга, о которой я тебе говорил" (Here is the book I told you about).
We are talking about one of your friends, and suddenly you see him coming. And you say to me: "Вот он!" (Here he is).

"вот" is used when you show something which is close to us. If that thing is far away, just say "вон" instead of "вот": "Вон гора". "Вон река".

Actually, "здесь" and "сюда" also assume spatial proximity. For distant locations, use "там" (there) and "туда" (to there).

Summary:

close to us: здесь (location), сюда (direction), отсюда (from here), вот (indicative particle).
far away from us: там (location), туда (direction), оттуда (from there), вон (indicative particle).

You can even combine "вот" with "здесь" (and "вон" with "там"):
- Где твоя комната? Вот здесь. - Where is your room? Right here. ("вот" assumes an indication gesture. It is optional. You can simply say "Здесь". It's also possible to answer "Вот.")
- Где гора Эверест? Вон там. - Where is the Everest mountain? Right there. ("вон" also assumes an indication gesture. It is optional. You can simply say "Там". It's also possible to answer "Вон.")

As you see from the examples above, it is most natural to put "вот" at the very beginning of a sentence (but not necessarily).

"вот" is also used without any specific meaning (as a filler word) in colloquial speech. Or it can imply that you are summarizing what was said before.
Example: (after some pause): ... Вот. Так о чём мы говорили? - ... So. And what we were talking about?
or you tell a story and finally, when you finish, you can add: "Вот." - It assumes you told everything you were going to tell.