The Scotland Office plays an essential role in managing day to day devolution issues between Westminster and Holyrood. The Secretary of State has recently described this work as 'oiling the wheels of devolution'. This is a process which requires close liaison across a wide range of Whitehall Departments to both promote and guard the devolution settlement, as well as regular engagement with key stakeholders in Scotland on a broad range of issues which are reserved to Westminster. A list of reserved and devolved matters can be found here.
The Scotland Office carries out an essential role on behalf of the people of Scotland in ensuring that when it comes to reserved matters - their voice is heard at the highest level in Whitehall:

This diagram shows the relationship between the UK Government (responsible for reserved matters) and the Scottish Government (responsible for devolved matters). It also shows that the Scotland Office is part of the Ministry of Justice, within the UK Government.