This medal is one of the Stars for the British Army in the First World War. It may have been the 1914+ Star or the 1915 Star or variation. To qualify the recipient would have need to have been serving in an active theatre of war between specific dates - dependent upon the particular star. If the recipient was still alive at the end of the war, then he would also have received the British War Medal and the Victory Medal.
You have the details: service number S-14276, S.O.M. (I do not know these initials) Sjt. (a short form for the word Serjeant (an older form of Sergeant). E. A. Vine(s), A.S.C. (Army Service Corps - later Royal Army Service Corps)
With these details you ought to be able to find the person via the Medal Record Cards (available on-line) or the Army Service Record or Pensions record, both of which are also now available on-line.
You might also go direct to where the original records are stored which are:
The National Archives, Kew, Richmond, Surrey, TW9 4DU • T: +44 (0) 20 8876 3444 www.nationalarchives.gov.uk
Army Personnel Centre HQ, Secretariat Historical Enclosures, Mailpoint 400, Kentigern House, 65 Brown Street, Glasgow, G2 8EX Help Desk • T: +44 (0) 345 600 9663