Definition of Meld
A meld in Gin Rummy is a set of cards representing 3 or 4 of a kind, or at least a 3 card straight.
A straight must have the cards all part of the same suit.
3 or 4 of a kind is commonly known as a "group" while a straight is known as a "run".
In this example there is a group of 5's and a run of 9/10/Jack of hearts.
The two 6's do not form a group.
You cannot share a card in both a group and a run. In the example below, the 5 of clubs can either be a group of 5's or a run of 5/6/7 of clubs. It cannot be both, you've got to choose one.
In this case you'd want to treat 5/6/7 of clubs as your meld as it reduces your hand by 18 deadwood points than the 15 deadwood points for the three 5's.
The same issue is represented by the 9/10/Jack of Hearts and the three Jacks. The Jack of hearts is shared by both the group and run.