Parallel play is when you and someone you like or love engage in separate activities near each other. While you may not necessarily directly communicate, you nevertheless enjoy spending time in each other's company.
Parallel play is a term used to describe a stage that typically developing children go through, where they play in the presence of other children without attempting to impact the other child's play. Autistic children, and some other neurodivergent or developmentally disabled children, tend to continue parallel play at older ages than their peers instead of engaging in cooperative play (playing with others). This is often pathologized, but there is nothing wrong with a preference for parallel play! Many autistic people continue to prefer doing activities in the presence of other people over doing activities with them. This can be a way that autistic people express or receive love-- choosing to do the same activity (such as reading a book) or different activities (such as chores, or one person doing a puzzle while another works) in the vicinity of one another. This can have the added bonus of providing a body double, which is when the presence of another person helps reduce someone's executive dysfunction so that they can get more tasks done!
Allistic vs autistic differences
The older allistic children are, the less likely they are to engage in parallel play and the more likely they are to play in groups/co-operatively. Autistics, on the other hand, are more likely to prefer parallel play even in adulthood.