Thiiiiiiis... REALLY is up to you. See, vibrations at their most basic are just the transfer of kinetic energy from one object to another in such a way that it produces periodic oscillations. So really, the ability to make objects vibrate at a distance is no different from telekinesis in practice.
The problem with this as it relates to your question is that telekinesis, and indeed superpowers in general, rarely have any clearly defined energy source. This is important because what you can and can't do with telekinesis is largely defined by how much force you can exert with it, which loops back to how much energy you have at your disposal.
Most authors never bother to explain where the energy for telekinesis and other superpowers come from of course (because there is no good answer). So that means that your telekinesis or your vibrations are as strong as you feel they should be. They rely entirely on the elementary transfer of energy between objects, and since you have no clearly defined source of energy (and thus no limits), your powers can be as strong or as weak as you want them to be.
If you're asking what applications vibrations as a superpower could be used for, you could theoretically cause objects to combust or explode by vibrating their molecules at the right frequency. Similarly, you can demolish buildings and other structures by making them oscillate at the right frequencies (in theory at least). Earthquakes might be another interesting avenue to look into but your character would need to be really powerful to do that.