Social Play is a little bit more difficult to nail down than the previous three, as it happens among all of the other types of play. You can engage in social play while using your motor skills (play pat-a-cake or explore the woods with someone), while creating (take turns telling a story, or build a blanket fort together), while engaging in fantasy play (sharing a dollhouse, or having another 'settler' join you in the garden), or (as you'll see with #5) when playing a game that has rules.
Baby's first play partners will likely be parents or other caregivers that understand the gentle and quietly stimulating play that they need. Later, children play alongside and then with each other. (You can look up "Stages of Play" on your preferred search engine to learn more about interaction and the social aspect of play, if you're interested). Like Fantasy Play, Social Play is one of the big building blocks of social and emotional development. Taking turns, cooperation and the full range of social rules are developed here, and though it typically occurs along with another type of play, it's vital to the healthy development of every infant or child.
Life can easily get in the way, but be sure to engage in some intentional social play with your little ones throughout the day: Read a book! Bang on pots! Stack some blocks! Explore a park! And, though it may be easy to assume their social play needs are being met by their friends and siblings once they start to grow, never underestimate the impact that playing with you can have on your child.
One tip: let them take the lead. Kids are directed pretty much through the rest of their day, so allow them to guide the play, even if you don't think they're doing it "right." If playing in the dollhouse means putting the tiny toilet on top of the wee bed and then making the dolls slide off the roof, that's okay! My three rules for intentional social play with kids are:
1) They can't hurt themselves on purpose. This includes things like jumping off of surfaces that are way too high. A good opportunity to model decision making and to find other risks to take instead.
2) They can't hurt someone else on purpose. A recent example in my mind would be a little one throwing balls at me as hard as they can. We found something else to throw at though, because it feels good to throw as hard as you can.
3) They can't hurt the toys on purpose. This does NOT include building towers just to knock them down, hahaha!
Other than maintaining these three simple rules, the pressure is totally off of you to direct the play: you can just enjoy playing socially, through the eyes of a child!