The phrase "to open out" means to expand or unfold in a particular direction. It can refer to something that is flat and two-dimensional, such as a map or book, being opened up so that it lies completely flat on a surface. In this sense, the term implies an action of spreading something outwards until it reaches its full extent.
The phrase can also be used figuratively to describe someone's personality or behavior opening up in a certain way. For example, if someone is usually very reserved and quiet but suddenly becomes more talkative and friendly, one might say that they are "opening out" socially.
Overall, the term "to open out" conveys the idea of something becoming larger, wider or more expansive in some way.