A terrific article by the American Academy of Pediatrics helps describe their behavior and offers strategies for coping with it.
Since I have twins in that age group, I'll be referring to this article often, and that's just at home. You can only imagine when we go to a playground!
Here are some of my favorite ideas:
1. Your child will be playing with other children more now, and dressing up in fantasy play. Sometimes they will still get in a tug of war over a toy/doll, or will tussle on the playground. Often their frustration gets physical. When that happens, don't let them hurt other children or themselves. Remove them from the situation, talk to them about their feelings and try to find out why they're so upset. Remind them of a time when they had their feelings hurt by someone or when someone hit them. Let them know you understand and accept their feelings, but that you don't like it when they hit other children. After they calm down and seem to understand, ask them to nicely apologize to the other child.
2. Your child will start to model behavior they see by other children doing. Boys will see conventional pictures of children on TV, in magazines, books and billboards. They will hear other families, friends and neighbors talking about what big boys or girls they are. Even if you are gender-neutral, allowing children to play with any toys they want, they'll get some guiding ideas from society in general. By the time they get to kindergarten, their gender roles will be formed so don't be surprised or upset by this.
3. By age 4, your child should have an active social life with friends and playmates. If they're not in a preschool or your neighborhood doesn't have children their age, go to a story hour at your local library. Try introducing yourself to other parents at the park and set up play dates. They'll enjoy when the kids come to your house and they can "show off" their home, their mom/dad, and their toys.
4. Realize that your toddler's friends are not just playmates but help them understand behavior and values. Believe it or not, by age 4, your toddler has a rudimentary idea of your values and even recognizes that there are other values and opinions besides yours. He or she may test these new discoveries by demanding things you don't allow like certain TV shows, clothing or toys. Don't worry if he or she is even rude to you for the first time, or uses unacceptable language. The best way to deal with it is to voice your disapproval and explain why you feel the rules you have in place are important. Take the emotion out of it. Many children adhere to rules because they want to avoid punishment, not because they realize that intentions are just as important as consequences. If you can take the extra time to explain it to them, it will help them grow more mature.
5. Make sure you give your toddler tasks you know they can perform and then praise him or her when it goes well. They can perform simple tasks like helping set the table or picking up their toys. They certainly want to be like older siblings who are doing household chores, so let them!