The way that a Claddagh ring is worn on the hand is usually intended to convey the wearer's romantic availability, or lack thereof.
Traditionally, if the ring is on the right hand with the heart facing outward and away from the body, this indicates that the person wearing the ring is not in any serious relationship, and may in fact be single and looking for a relationship: "their heart is open."
When worn on the right hand but with the heart facing inward toward the body, this indicates the person wearing the ring is in a relationship, or that "someone has captured their heart".
A Claddagh worn on the left hand ring finger facing outward away from the body generally indicates that the wearer is engaged.
When the ring is on the left hand ring finger and facing inward toward the body, it generally means that the person wearing the ring is married." 
CLADDAGH RING ORIGIN
are a variety of legends about the origins of the ring. One tale is
about Margareth Joyce, a woman of the Joyce clan. She married a Spanish
merchant named Domingo de Rona. She went with him to Spain, but he died
and left her a large sum of money. She returned to Ireland and, in 1596,
married Oliver Ogffrench, the mayor of Galway. With the money she
inherited from her first marriage, she funded the construction of
bridges in Connacht. All this out of charity, so one day an eagle
dropped the Claddagh ring into her lap, as a reward.
Another story tells of a Prince who fell in love with a common maid. To convince her father his feelings were genuine and he had no intentions of "using" the girl, he designed a ring with hands representing friendship, a crown representing loyalty, and a heart representing love. He proposed to the maid with this ring, and after the father heard the explanation of the symbolism of the ring, he gave his blessing.
One legend that may be closer to historical truth is of a man named Richard Joyce, another member of the Joyce clan and a native of Galway. He left his town to work in the West Indies, intending to marry his love when he returned. However his ship was captured and he was sold as a slave to a Moorish goldsmith. In Algiers, with his new master, he was trained in his craft. When William III became king, he demanded the Moors release all British prisoners. As a result, Richard Joyce was set free. The goldsmith had such a great amount of respect for Richard Joyce that he offered Joyce his daughter and half his wealth if Joyce stayed, but he denied his offer and returned home to marry his love who awaited his return. During his time with the Moors he forged a ring as a symbol of his love for her. Upon his return he presented her with the ring and they were married." 
 Murphy, Colin, and Donal O'Dea (2006) The Feckin' Book of Everything Irish. New York, Barnes & Noble. p.126 ISBN 0-7607-8219-9