I felt broody, from about the age of 14 until I had DS at 20. It was a feeling of being empty, feeling like something was missing, that I should have that heaviness in my arms. I used to sleep on my front or put pillows/heavy fabrics across my stomach so I could feel a kind of pressure there, mimicking the feeling of pregnancy. I used to read child development books and childcare manuals secretly in the library/bookshops because I thought people would think I was insane, and I also read every book about teenage pregnancy that I could.
If I ever held a baby or even the weighted doll things they have for schools, that made it even worse and stronger. I always had really strong ideas about how I'd do stuff as well. Funnily enough I loved every minute of pregnancy to 0-3 years old, after that it got tough, I suppose because I hadn't really considered that age, but also because I'd expected my only child to have a sibling by that age too, which I think would have helped.
Interesting that someone mentioned it being about wanting to create a family atmosphere you never had. I had a small family, just me, DSis and DM. I always wanted 5 children, a big, busy, happy family with everyone crammed into bunk beds. Instead I'm married but have one child from a previous relationship who is 6, so no close in age, and probably not loads more. Two more maybe. I latched right onto DH's big, busy, annoying but lovable family too as soon as I met them. Parenting wise, I find the practical stuff harder than I'd thought I would and the having to be grown up part is hard too. Probably partially because I was so bloody lax with contraception and had DS at 20 in an unstable relationship, thinking it didn't really matter if the dad swanned off because I'd have this great strong single mum thing going on. Nope, it's hard. News flash 
I have never again been as broody as I was before having DS, I won't take risks like I used to, if I could absolutely rewrite my life I wouldn't have had him when I did, I can see now it was utterly stupid to give in to those feelings. By giving into hormones and the whims of a careless partner I robbed myself of the busy, happy family I could have had, because we're just never going to catch up financially in order to be in a position to do it, and I'm never going to catch up personally to have the energy and patience to be able to do things the way I want to, and plus I never got to have a pre-children adult life.
DH has been broody since he lost an unborn child at 16.