Frankincense is a resin mostly used in churches but can also used for eating. It is said that it has also a medical impact on your body. Because it is not totally researched what kind of side effects you have to expect you should not eat the whole of it. Frankincense has a really strong bitter taste so you should be careful otherwise you will ruin your whole meal. This happened a couple of times when I was trying out new stuff.
Maybe you should just read the Wikipedia article.
Mastic is a resin mostly produced in Greece and used in Greek kitchen for example to make Retsina. It is worse it to read the Wikipedia article.
Resin usually has a really strong taste so it is easy to overdose and totally destroy the food. So its better to use as less as possible.