The Stamina Vessel is an item featured in Breath of the Wild. It is similar to the Heart Container, but instead of increasing hearts this adds another 1/5 of a wheel to the Stamina Wheel.
From Goddess Statues
Increasing Link's maximum Stamina
"The size of your Stamina Wheel has been increased, allowing you to perform more actions before getting tired."
These can be obtained by exchanging Spirit Orbs with any of the various Goddess Statues found in Hyrule. If Link has the maximum amount of hearts (3 preset + 27 additional) when he completes a Divine Beast, a Stamina Vessel will be rewarded in place of a Heart Container.
When Link visits the Horned Statue, located in Hateno Village, he can sell a Stamina Vessel or a Heart Container in exchange for 100 rupees. The statue will then allow Link to purchase either a Heart Container or Stamina Vessel for 120 rupees, allowing him to swap between the two at a net cost of 20 rupees.
Link can obtain a maximum of 10 Stamina Vessels in order to gain 2 extra Stamina Wheels. As shown in the graphic, should the player choose to have full health, a maximum of 7 Stamina Vessels can be gained because there's only so many slots to allot for each type of vessel.
An additional Container/Vessel can be obtained with the completion of the DLC-exclusive EX The Champions' Ballad, which awards an extra four Spirit Orbs.