In essence an authentic context is one that is 'real' (authentic) and that the students perceive to be of importance to them. It increases engagement of the students involved and also encourages them to link new learning to what they already know in other contexts that they are interested or engaged in.
The difficulty for teachers here is that they have to be prepared to truly listen to students, and constantly look for opportunities to bring their students' worlds into the classroom. This means that as teachers we need to change from focus of planning and teaching from 'learning drives the context we teach in', to 'the interest and lives of students guides and drives the context of learning'.
Simply put, teachers and students need to find ways to discuss and choose contexts that relate to them. One quick way is to just simply ask. This could be as a whole class brainstorm, small group or individually.
In digital classrooms there are some fantastic brainstorming tools that can be used to easily collect student ideas including ones;