What is the "power" a PhD advisor has over their advisees?
In many programs, the advisor signs off on the PhD student's thesis. If the advisor doesn't approve the thesis, it is difficult to impossible for the student to graduate and earn the PhD.
In many programs, the advisor is responsible for securing funding for their PhD students. If the advisor withdraws funding that the student was expecting, the student might not have another source of financial support. 
Advisors are responsible for training and mentoring their PhD students, which is a major part of the PhD. If an advisor withholds that training, their PhD student might not become a successful researcher without it.
In general, advisors interact closely with their PhD students. If these interactions are unpleasant or abusive, the workplace becomes very, very uncomfortable.
Faculty tend to have a lot more influence in an academic department than their PhD students do. An advisor can potentially make things difficult for their PhD student with other faculty in the department.
In many cases, on applying for jobs after a PhD, a student is expected to have a recommendation from their PhD advisor. Without it, it can be much more difficult to find a job. Also see: How to handle not having my PhD advisor as a reference? and What to do when a thesis adviser refuses to recommend me?