For these questions you should google the ESRC Postgraduate Funding Guide. To save you the time:
'Since October 2006, new students in receipt of a ESRC standard studentship award (undertaking advanced quantitative methods training during the PhD can make a case for an enhanced stipend of £3,000 per annum (conditions apply).. The Research Training Support Grant (RTSG) for AQM award holders will also be increased from the standard rate of £750 per year to £1,000 per annum. This is to support cost of training in advanced quantitative methods.'
So it implies that it is for the training cost. As for how it actually it works... there will be someone at your university responsible for ESRC studentships, and they would be the person to ask.