Like it-ogo already explained, "вот" is used when you want to point at something or when you are handing things to others.
"Здесь" is more about location and it means "here/at this place".
Here are (вот) a few examples that illustrate the difference. No pun intended :-)
Вот зонтик. = Here's the umbrella.
Зонтик здесь. = The umbrella is here.
Передай, пожалуйста, соль. Вот! = Pass me the salt, please. Here you are!
Где соль? Здесь, на столе. = Where's the salt? Here, at the table.