Fairgame, there is no English General Election, it's UK-wide, and people in Scotland, Wales and Northern Ireland all vote. No party stands in all parts of the UK. The SNP only stands in Scotland, and Plaid Cymru only stands in Wales; similarly the Democratic Unionist Party stands only in Northern Ireland, as does Sinn Fein.
All of these parties send Members of Parliament to Westminster (well, except SF, but that's besides the point) and these MPs represent their constituents. Supposedly each MP has the same voice as any other MP, so an SNP MP has as much say as a Labour, Tory or LibDem MP. It's just that, historically, there have been many more Labour/Tory MPs, so other voices haven't had much influence.
This time round, neither Labour nor Tory look like they'll have enough MPs to form a majority government, so both must look to the smaller parties for help. The SNP are expected to return an unusually high number of MPs; the last Parliament they had only 6, but polls are predicting that they might have as many as 40-50 (out of 59) so they may form a significant group.
The SNP have stated that they will not support a Tory gvt, but are willing to work with Labour on a case-by-case basis. Neither SNP nor Labour have expressed a desire for a formal coalition, such as that between Tory and LibDems last time round.