As parents we feel pleased when we see our toddler willingly and graciously sharing her toys, disappointed if we observe selfish behaviour, and appalled when somebody else's child is overly possessive with his toys.
As parents, nannies and child care professionals though we need to understand that sharing is not an innate behaviour, but something that is learned at a particular stage of development.
Before sharing, toddlers must first comprehend the concept of ownership. You'll know that she is working on this when she starts saying "Mine", this will probably start around the age of two years old. Ownership demonstrates autonomy and a sense of self, and as paradoxical as it may seem, she needs to develop this before she can begin to understand sharing. In between developing a sense of self and a willingness to share, toddlers will begin to show their toys with others but without actually letting the other take possession. When you see your child showing a toy to another, you can gently encourage sharing, but don't force it. She will share when she is ready.
If you feel frustrated by what seems like the slow progress of sharing behaviour, here are some tricks. Set up a play date with other children at your house. Go through her favourite toys one by one and allow her to select some of her most special toys which she would rather not share with others and put them out of sight. Then explain to her that she should share the other toys with her guests. Explain that having play dates is fun, but that you can't very well have a play date if you don't have plenty of toys to play with. One trick is to organise games in which sharing is an essential part of the game, such as tossing balloons or passing balls or swapping roles and toys in a game of doctors and nurses. Art activities can can be cooperative affairs, especially if each child has their own set of materials. You probably soon will observe some swapping of crayons or sharing of a particular colour.
You may also notice different behaviour in different settings. You child will probably be far more possessive of her things in her own house, but may act with more generosity and social graciousness outside in a park or somebody else's home.
Children tend not to be comfortable with cooperative play until around four years of age, but encouraging two to three year old kids to share is quite OK. You will almost certainly have some measure of success even a small amount of which will make play dates far more enjoyable for both the children and the parents.