Flu is a nasty piece of work. DS had it early this year. He missed over 3 weeks of nursery and spent most of that time in my bed. He was drained, raging temperature, didn't eat, lost a load of weight, it was awful.
Children are excellent spreaders of germs. They go home and spread said germs to parents, grandparents, siblings etc.
Immunising the spreaders can help prevent spreading the virus (immunise those most likely to catch it and spread it to protect the rest of the herd if you will). Think about it. I work from home. DS goes to a school with 150 other kids, plus staff. Who is more likely to come into contact with flu virus, catch it and spread it? Me or DS?
Young children often have asthma (more so than older ones) which can be exacerbated by flu.
The vaccine is a "inactivated" or watered down version effectively, meaning it does not give you flu. Your body identifies it as germs and creates antibodies to fight the nasties.
Downside is that flu is a virus, it mutates, creating flu's with different genetic codes, so new vaccines need to be created to have the above effect, eg if you have a vaccine for flu type x but you catch flu type y, vaccine x will not prevent you from getting that flu (y). Scientists monitor and try to assess which viruses will be doing the rounds and create vaccines accordingly.
After the episode earlier this year where both DS and DH had it, we are going to get the jabs.