I have an aechmea blue rain

Welcome, Dawnieballs!
Sooner or later, bromeliad (including Achmaea) flowers die, then new shoots grow from the mother plant, while she slowly turns brown and dies also. The new babies will grow for 2-3 years, and then bloom themselves. If you can get a good-sized clump going, you will get at least a few flower spikes every year. To grow the babies on to blooming size, give them very bright indirect light or some filtered sun, let the compost dry out almost completely between waterings, and give them some humidity, Feed them lightly once a month with a good low phosphate houseplant fertilizer. When you repot them, use a coarse, fast-draining compost such as cactus mix, or Cymbidium mix. Hope this helps!

In addition, I believe that the dying parent rosette diverts a lot of its stored food reserves to the new offsets at least initially.

True. If the flowers aren't pollinated by a certain time--fairly long in bromeliads--the plant doesn't waste much energy on maintaining the old flower stalk.

Thanks guys very much appreciated

How do i take the cuttings

I was bought one of these as a moving in gift in Sept 2013. It had a huge, beautiful flower which died towards the end of 2013, however, the mother plant has since produced 10, yes 10, babies and they keep on coming! Mother plant is still nice and green and healthy and showing no signs of stopping producing babies anytime soon. I am running out of people to give them to! To anyone who has babies growing, wait until they are approx. 1/3 the size of the mother plant, then break them off gently as low down on the mother plant as you can then simply re-pot in a medium sized pot with plenty of room for growth. Not sure how long babies take to flower but I know once they flower you should water into the cup of the plant rather than the soil.

Thanks for all the advice Snooki. Really helpful.