Nobility are those who have rank or privilege due to titles, positions and/or land that has been won through marriage, battle or birth, or has been awarded by the Crown or other nobles.
Nobles in the SCA
In the SCA, everyone who plays is regarded as being a noble. However, titles must be earned (eg. Award of Arms, peer). Like real life, there are various levels of nobility, but you are often only as noble as other people think you are. Your blood may make you technically a noble but your attitude may make you an arsehole.
Nobles in Re-Enactment
In re-enactment portraying nobility may be restricted in some manner. Usually this will be based on the strength of their portrayal of someone from the period in question (ie there is no point saying that you are a noble if you dress inappropriately) or on the physical limitations of the time and location (ie American Civil War re-enactment tends to be pretty light on nobles).