Your bloodline is your heritage or ancestry. In other words, your bloodline includes your parents, grandparents, great-grandparents, and so on.
You might talk about the bloodline of a show dog, bragging about the pedigree of your funny-looking terrier. Sometime a horse's bloodline is also a selling point, particularly when someone is betting on a race horse. You have a bloodline too, although the word more often describes the heritage of a famous or royal family. The Old English root word blod, means "blood." By the 13th century, blood also meant "family" or "heritage."