Here is a few images of what a Boston Terrier and a Beagle mix puppy looks like.
In terms of appearance they have short hair and a small but strong build. They have a square head and large ears and feet for its size. They are usually brown, white and black.
These dogs can take on any number of the characteristics and looks of either breed, so each one will look different from another, also with different temperaments.
It also depends on if the dog is 50% Beagle and 50% Terrier, which they are often not. In many cases the dog will be more of one breed than the other, so will also look more like one breed than the other.
It is well known that they are very loyal, friendly dogs. They are also not very easily frightened and love spending time with people.