Hi, 

Some additional photos of the entire tree could be helpful. 

It is a type of cherry tree. The branch could have broken from the weight of new growth and leaves combined with wet or windy weather. It doesn't necessarily mean it was diseased - we can't see any signs of disease or pests from this photo. It could have been from improper pruning, or a growth pattern that wasn't corrected. 

You should remove the branch with a clean cut so the tree can grow callous tissue and essentially heal properly. Trees don't heal their bark like human skin, but it can hard the wood harden and form around the wound so bacteria, fungus, or insects don't infect the inner wood. Leaving the broken branch reveals an entry for these issues that could become problems down the road. 

If it is overhead or large branch we would recommend using a licensed tree expert  or certified arborist to remove the branch so it is cut properly and safely. Additionally we have some information on how to remove larger branches so they don't break further when cutting if you can easily reach it and are confident to cut yourself. 

Emily