False awakenings are a common thing among dreams, specially those who intend to become conscious within their dreams.
Why do they happen? I guess no one really knows yet, but they are a precursor to becoming conscious in your dreams and are a definite dream sign that really should spark that critical thinking within your sleeping mind, to wake you up to the fact that you are indeed dreaming!
But what is a false awakening? Well, it is simply a dream where you wake up from a dream, and you dream of waking up in your bed. Some things may seem really odd, like your room is a mishmash of other rooms in your house.
However, these are good signs as having a false awakening is a good indicator that you are dreaming and many lucid dreamers become lucid through such awakenings, myself included.
It is entirely possible to have multiple false awakenings in one dream, and I believe it is your subconsciousness way of telling you it is time to wake up to the fact that you are in a dream and to take control of the situation.
Of course, doing a reality check as soon as you wake up is a good habit to have, something I do regular now just in case I have had a false awakenings but in truth, after a while you do begin to recognise the dreamscape, you do begin to get an inkling that things are not quite normal as they are in waking reality!
My first false awakening happened after my third lucid dream, and since then false awakenings have become a regular occurrence, and often lead to many more lucid dreams than I would otherwise have missed had I been so nonchalant to them.
You can induce a false awakening, and it is simple to incubate one; before you go to bed, imaging that you will wake up in your bed while dreaming, and then performing a reality check! The mere act of imagining a false awakening should prompt one to happen, and in turn prompt you to become fully lucid, given that you already do reality checks, dream journals, so on and so forth!