Bloodlines are anomalies of the DNA that allow the wielders unique abilities, e.g. enhanced chakra control, enhanced stamina, regenerative effects, improved elemental control, etc. The name of the bloodline typically describes both the anomaly and the resulting techniques associated with it. Historically bloodlines are passed down between generations, however, in the modern age of the ninja world it is possible for non-bloodline ninja to acquire the genetic traits of bloodlines through ninjutsu-assisted surgery.
When you reach the rank of Genin, you can go to the hospital of your village to take blood samples, in order to learn whether your character was born with an innate bloodline. If not, it is also at the hospital where they offer the service of implanting bloodlines into your body.