In general, there are two options for that.
The first option applies only to primitives - during the customization of each object, you have the option to increase the number of segments creating the object, which will smooth out the curved surfaces when possible. However, it's not perfect, as even the smaller faces will not give you the perfectly round look you might be looking for. In such cases, look at the second option.
The second option relies on changing the display of the object to make it appear completely smooth. You can do that by enabling the Smooth display option for the entire object, but this way, you will lose all the sharp edges of the object.
To avoid that, it's much better to select the part of the object you want to smooth out first (in the case of this cylinder, we want just to smooth the horizontal faces), enter the Materials section, and enable the Smooth Shading for the selected part, and decrease the Shinines as well for the best effect.