It means that the company which underwrote your warranty may pay for the repair. It depends on whether they judge the failure to fall within the terms of the warranty (based on their inspection), or that it is due to general wear & tear or abuse.
You should consider yourself unlucky that the gearbox has failed, but looking on the positive side – it has failed during the warranty period.
I would check the warranty terms – you might still have to pay an excess of £50 or so towards the repair. I would very much doubt that the selling garage did not check the gearbox oil, or that any claim would be rejected on the basis of a service not conducted (over the two months you have owned the car).
Personally I would expect the warranty to pay out – your problem will be if they refuse. Your only route to contest this would be to pay for an independent inspection. Before taking up such an option – you should get agreement from the warranty company that they will agree to cover the repair, should the independent inspection find in your favour. Otherwise, you would have to take legal action to reclaim your costs.