This term is contained in Italian accounting standard: OIC 28: Il Patrimonio netto http://www.fondazioneoic.eu/wp-content/uploads/downloads/201...
Unfortunately the Italian term itself gives little indication of what it means except that it is a reserve which contains a balance on current profits.
OIC 28 states: ” tale riserva accoglie il rateo di dividendo pagato dal socio che ha sottoscritto un aumento di capitale sociale in corso d’anno"
The "rateo di dividendo" is the divided accrued, which affects the share price. A share price should fall after a dividend is paid because it is worth less.
When the share capital is increased with a rights issue, the part of the proceeds which represent the accrued dividend goes into this reserve, while the main part goes into the share capital account.
How to translate? A literal translation would be as misleading and confusing as the face value of the Italian term. A meaningful translation. "Reserve for accrued dividend portion of share capital increase"

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Note added at 1 day6 hrs (2017-08-16 05:21:45 GMT)
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Basically, shareholders pay money to the company to buy new shares. Most of that money goes into the share capital account, but a portion goes into a reserve to help pay part of the dividend due after the end of the year.