The blanket is a layer surrounding the vessel in a fusion powerplant. It will absorb the energy from the fusion neutrons produced in the plasma, boiling water via a heat exchanger, which will be used to drive a steam turbine and produce electricity.
The proposal is to embed lithium in the blanket, because that will react with the neutron to produce tritium, which is a fuel for the plasma, along with deuterium. The breeding of tritium occurs through the reaction Li6 + neutron becomes He4 + tritium. This would be advantageous because tritium is radioactive, with a short half-life, and so is difficult and expensive to obtain – it would be far more sensible to manufacture it onsite as a by-product of the fusion process.