Many lenses these days — especially zoom lenses — have some type of stabilization on them. It is usually labeled as IS, OS, OIS or VR, and it can be turned on or off with a switch on the side of the lens.
This feature is beneficial for hand-held photography, and will oftentimes give you an extra stop or two of light (for example, with stabilization turned on, you might be able to get away with hand-holding a 200mm lens at only 1/60s or even longer).
However, when using a tripod, the stabilization feature works against you. In order to get sharp, movement-free images on a tripod, be sure to flip that switch or setting to “off.” When your camera is perfectly still, but the stabilization feature is turned on, it still tries to keep the lens stable and the tiny movements of it doing just that will actually shake your camera ever so slightly.
These images show an example of my Fuji X-T1 and Fuji 50-140mm lens (on a tripod) with the OIS turned on:
Then, I turned the OIS off and the image was sharp: