Goffman's initial discussion frames social interaction, in person specifically, as a performance. Subsequently a sequence of metaphors about theater ensue. The people are actors playing roles. The venue of social interaction is the stage. And the performance is two-fold. As a participant, each person desires to protect their reputation and public appearance. On the other hand, individuals are also trying to learn as much as possible about the people around them.
Remarking upon intent, Goffman outlines how each performance is a risky endeavor. People are trying to save face and avoid embarrassment. To this end, entire groups or teams are formed which help individuals align according to their common style of performance. With such high risk, it seems initially odd that people engage in social relationships, but the reward of discovering knowledge about other people proves worthwhile most of the time.
The curious thing about social performance, in Goffman's esteem, is that the theatrical metaphor breaks down in the reciprocal nature of relationship. At any given moment, folks are both performer and audience. People are all, collectively, engaged in a performance, which often causes unspoken diversions from honesty. For example, if a person trips at a fancy dinner party, the other people at the party may not acknowledge that the person tripped. Their goal is to make the performance a success, so they are likely to help the individual save face. Goffman finally dips into social science by observing that within the structure of the performance, the individual retains a good amount of agency to craft an experience for their audience.