You know that "Have" often means possession. "You have the ball." But that is not how it is used here.
"Have" can also mean some status or relationship for a thing.
- "Be sure to buy the bread they have on discount." (status: lower cost bread)
- "I prefer the music they have on the radio." (relationship: music played on radio)
- "The police have him under surveillance." (status: police watching him carefully)
About "on hold":
Some stores allow customers to pay small amounts over time for expensive things. This is called putting the item "on hold". "On hold" is the status of the dress, as long as Monica makes regular payments. It means the store will not sell the dress to anyone else, allowing Monica to have time to pay the full price. Now Monica has her final payment and is ready to pick up the dress they have "on hold".