An "oak barrel" is a barrel made of oak in which wine is aged.
Oak is a general term for the Japanese oak tree, and the types used for aging wine are called "French oak" and "American oak."
Oak barrels allow a small amount of oxygen to pass through, causing the wine to slowly oxidize. This causes complex changes in the wine's flavor, aroma, and color. This change is called barrel aging (sometimes called barrel maturation).
In addition, barrels are made by charring oak wood over a fire, which gives the wine inside a charred, dark flavor that imparts aromas of toast and caramel to the wine.
Generally, the newer the barrel, the stronger the aroma, and the longer the barrel is used, the milder the aroma becomes. Wine producers choose the barrels they use to suit the characteristics of the wine they are aiming to create.