The context of an improvisation performance is most basically ‘that what is present‘.

This includes the concrete entities in the location of the performance:

• the space itself
• the people (performers and audience) present
• all objects (instruments, furniture, coffee cups, lamp posts, etc.)

It might also include more ephemeral entities, like the history of the building that can be felt, the remembrance of what happened in this space a few hours ago (which are both aspects of Memory), and more of such intangible things.

One way to approach improvisation performance is to state that all entities in the room at the beginning of the performance are the ‘score’ or the ‘script’ of what is about to happen in the unfolding piece.

This could be either an implicit agreement or understanding (that you assume all improvisers share, which we could call a Common Ground) or an explicit agreement that you explicitly create for the performance (by expressing it to your fellow performers, then it becomes a rule or Structure).

Note that there always are implicit agreements / unspoken assumptions about ‘that what is‘, there are always ideas in the heads of performers and audience about how to engage with the situation, whether you want them or not. For example, an audience will always implicitly assume that they shouldn’t enter the performance area. Even if the performance area is not clearly defined, they will mostly arrange themselves at the edges of each space they enter, unless there are clear visual cues or other instructions that gives them permission to overrule this unspoken (social) agreement.

Read more about context under

IMPLICIT AGREEMENTS (Common Ground)
EXPLICIT AGREEMENTS (Structures)