In short, they bred 100 of these male mosquitos up and found that when females bred with them they ended up laying infertile eggs. Females only mate once in their lifetime, and thus will produce no offspring if they make the mistake of pairing up with a dud male. The males are expected to also potentially have a benefit over other male mosquitos who do produce sperm. The sterile mosquitos may invest their energy into other areas of their survival if they aren't able to invest it into sperm production.
The trouble is that one needs to breed up effectively millions and millions of these males and then release them into the wild in the hopes of outcompeting fertile males. Assuming this could be done, the numbers bred up and then released into every area where Malaria exists, there would still be at least a small portion of fertile males mating with females. The sterile males would die and not pass on their sterile genetics (because they can't produce sperm to pass on their genes...). So all you'd need is just one fertile male mating with a female and Malaria could still be spread, however the million or so annual death toll from Malaria would definitely be substantially reduced.
Treating any pest problem with genetically infertile individuals is very difficult as they can't pass on this trait.
I think they need to focus on breeding a mosquito that has a genetic mutation that disallows transmission of Malaria. In other words, they can't carry the parasite. If you could their introduce this strain, after having decimated wild mosquito numbers, hopefully it would become the dominant strain of mosquito. That or work on a vaccine like treatment.
I might add just as an FYI, that Malaria is a unique disease because it is caused by a protozoan parasite that gets into your blood named Plasmodium flaciparum. At our university one is able to study the species through the botany department.