What does waitlisting mean?
Let's start with the last question first. Schools typically offer places to more applicants than they have places for, on the theory and experience that they will have enough acceptances to fill their empty seats. In the event that they have fewer acceptances than they expected, the waitlisted candidates are offered whatever places are available. What are your chances of being offered a place if your child is waitlisted? The most competitive schools are least likely to offer places to applicants on their waitlists.
So, if your first choice school waitlists you, what do you do? Treat that as a rejection because, for all practical purposes, that is what it is. Accept a place at one of the schools which has accepted you. Don't give it another thought. After all, you have already determined that all the schools you applied to were great 'fits'. That's all that matters. Be content with the fact that your first choice thought highly enough of you that it waitlisted you.
How to avoid waitlisting
Are you just beginning the process of choosing a school for your child? Then keep the idea of waitlisting out front as you begin to define the list of schools you would like to consider. That last should include three categories of schools: schools which are very competitive or a reach; schools which your child stands a good chance of getting into and schools which are almost certain to admit your child or safe schools. When you develop your short list of schools this way, you won't be disappointed when one of the very competitive schools rejects your child outright or possibly waitlists her. Put another way, you want to look beyond the competitive schools as you explore all your options and develop your short list of schools to actually visit. That will minimize disappointment and stress when the acceptance letters come out in March.
Be realistic as you develop your list of schools. The safest course of action is to hire a professional educational consultant. She knows her schools. She knows which ones will be a good fit for your child. Listen to her advice and recommendations. You will get good results.