Hi Gab66, hopefully you've been able to join the Choosing Breast Reconstruction group and had a chance to check out the Reclaim Your Curves website.
As @primek said, the type of surgery you are being offered is a Lat Dorsi Flap reconstruction (
http//www.reclaimyourcurves.org.au/latissimus-dorsi-flap.html) which uses the large lat dorsi muscle from your back to make a new breast. It is usually paired with an implant to make enough volume for a reasonably sized breast and my guess is that because you have had radiation the surgeon you have seen is offering this type of flap reconstruction as an implant-only reconstruction can sometimes be compromised by radiation (although not necessarily always).
You should also be aware that a lat dorsi recon is not the only tissue flap reconstruction available but some surgeons do not perform the other procedures such as the TRAM or DIEP reconstructions as they require specific micro-surgical skills and equipment. Lots of women in our recon groups have found it useful to talk to a few plastic surgeons to fully understand the options that are available to them. Talking to other women about the different options and what reconstruction might best suit you is helpful, so feel free to post any questions you might have in the Recon group as there are a number of women who have had both Lat Dorsi and implant-only reconstructions (including after radiation) that you might be able to connect with.
Best wishes, getting your head around all of this can be overwhelming but we are here to try and help. Jane xx