when building my lein to roof..?

A birds mouth connection keeps the connection from shifting under loads, such as wind loads, up to a point of failure. A tied connection will shake itself apart under sustained winds. Simpson strong ties will work up to the point of sudden failure. So will Hurricane connectors. With a well designed wind there is no structure which will resist it except an underground concrete bunker.

You can form this joint in a number of ways - and by using various connectors.

You need to prevent the end of the rafter sliding off the wall plate and you also need to stop it lifting.

A birdsmouth is commonly used because it is cheap - you just skew nail into place.

But in any event you need to strap the roof down - look at something like Simpson connectors.

In most parts of the world you need building consent - details of these are usually included.