Здесь = In this place (here)

Вот = Here it is (here)

In some situations the can be almost interchangeable, in some not.

Вот мой дом - Here is my house (You are standing in the close proximity and pointing to a building).

Здесь мой дом - I live here (You are standing inside the house). If you are not standing inside a house "Здесь мой дом" is likely to refer to the area or the city.

Вот ручка - here is a pen (your are giving a pen to somebody)

Здесь ручка - would sound strange. You can say "здесь есть ручка", which would mean "There is a pen in this place"..

If I remember correctly, здесь is "here" in general, while вот is the "here" you use when kind of showing something (like: вот мой дом = here is my house). There are comments about this under Discuss sentence which explain it better.

Здесь means just "here" "in this place" Приходи здесь со мной - Home here with me.

Whereas "Вот" is more of an expression. Like "Here you go" "There we go" Вот, нашей ребенок является лучшим" -"There we go, our kid is the best" Вот, здесь ваша гостиница." - Here we go, your hotel is here"

Понимаешь? :)

Здесь means "here" as a place . "Здесь мыши!" - There are mouse ! "мы остановимся здесь" - we are staying here

Вот can be used with the Здесь either "мы остановимся ВОТ здесь" we are staying right here "ВОТ здесь мыши!" - Mouse are right here

Вот can be used also to underline next word - Вот так - That way - Вот дурак! - he is a true fool.

in some context вот can mean Здесь , but it is just omitting Здесь - Где пиво? - Where is a beer? - вот! (вот здесь) - here you are or - да вот [здесь] же ! - meaning open your eyes and look here