A double refers to a room with one large bed and a twin room contains two smaller beds. To confuse matters, some hotels may use the term "double" for any room housing two people without regard to the bed type. In order to avoid confusion, travelers should always check with hotel management to make sure they're renting the specific type of room they require.
The Better Sleep Council says twin mattress dimensions are approximately 38 inches wide. A full mattress (also called a double mattress) is 53 inches wide, 15 inches wider than a twin. Both twin and full sizes are approximately 75 inches long, which may not be long enough for taller individuals.
A couple traveling together would likely prefer a double room so they can share the bed. Other travel partners may prefer a twin room with separate beds so they can sleep apart. This is why the double room is often said to have "matrimonial beds" while the twin room consists of single beds. When a family is traveling, the parents would take the double room and the children would take the twin rooms. The two twin beds can always be pushed together if necessary.