A db extension usually indicates some sort of database file.
Lots of programs use it, sometimes as an internal file to store a list of things and not usually expected to be opened by the end user.
To be honest without more information it is going to be dificult to say what program could open it.
Could you not ask the person who sent it to you what type of file it is?
It is not called thumbs.db is it?
Here is a list of programs that use the db extension, but it could be any of them, or none of them.
http://filext.com/file-extension/DB