An Off-Zel vase
A vase was a type of pottery which was used for displaying cut flowers. Vases were either plain or decorated and were made from various materials, including metal. They were typically made by potters in a workroom. One well known type of vase was that made by Mark Off-Zel. (TNG: "The Most Toys")
Several vases at the monastery
The atrium and the reliquary of the Vulcan monastery at P'Jem stored and displayed several vases. (ENT: "The Andorian Incident")
During the Occupation of Bajor, when a vase was overturned, it was a signal for resistance fighters of the Bajoran Resistance that someone had a request which could only be answered by the Resistance. This simple communication was used for years aboard Terok Nor, during the administration of Gul Dukat. (DS9: "Things Past")
In 2370, Data's pet cat Spot broke a vase in Geordi La Forge's quarters. (TNG: "Force of Nature")