Vibrations can have multiple causes.
Common sources of vibration is a wheel or tire being out of round, a wheel being out of out of true or a wheel being out of balance. If the tire was mounted in such a way that it is not an equal distance from the rim, this can cause the wheel as a whole to be out of round (i.e., a “hop”), which will be felt as vibration, especially at speed. Similarly, damage to the rim (e.g., striking a curb) can cause a similar hop and vibration. A wheel that is out of true can also cause vibrations as it will move laterally through the wheel rotation, which will shift the bike and rider laterally and will feel like a “vibration” to most riders. Finally, if the rim is substantially unbalanced in terms of weight (i.e., one part of the wheel is heavier - e.g., reflectors) then the wheel can vibrate at speed. Some speeds can hit the resonance frequency making the vibration particularly more noticeable at a certain speed (e.g., 40 kph). Most people do not balance bike wheels, as the effect is typically small.
None of these problems are as serious as the final type of "vibration" which is typically referred to as a “shimmy.” This is essentially an unintended steering oscillation and if it gets out of hand (i.e., hits resonance frequency), it can easily cause riders to loose control. The cause of bicycle shimmy is not fully understood, but tubing flexibility and bicycle geometry seems to play an important role (i.e., some geometries produce more stable designs, and a stiff top tube can reduce the likelihood). Tire size can also contribute (i.e., pneumatic trail). This problem is typically rare in modern bikes.
Even though shimmying is rare, I would suggest spending some time to rule it out. For example, put the bike on a stand and spin your wheels up to speed and look to see if the wheels is spins true, the outside diameter is round (i.e., no hops), and the wheel otherwise does not exhibit excessive vibration. If the wheels are fine then you may be experiencing shimmy, which is a concern. This would largely be the result of the bike design (typically not enough trail or weight in front of the steering axis), that said, there are options to lessen the effect, such as dampening the steering response through the use of roller bearing headsets. Again this type of issue is rare, and usually associated with more boutique bike geometry, such as the low trail randonneur bikes from the 1950’s.