People in a childcare setting need to work together to ensure that all of a child's needs are met, as they cannot fend or provide for themselves, and that they are sufficiently protected. These children will rely on your for help and support and as a member of the setting that they look up to, you are collectively responsible for that child's welfare.
Teamwork is the ultimate tool that will help children grow into strong, independent, friendly young people so that when they enter school and environments with other children, they can work well with them and be sociable. Setting them up with these skills when they are younger will give them more of a chance at succeeding in life with what they want to do.
As mentioned before, children are very impressionable at a young age and if they see their family or people around them not co-operating and working together, then they are going to learn this behaviour and think that this is the right way to behave.
You will also be teaching the children to communicate as this is not something they can do straight away so you need to make sure that you set a good example and communicate well with your colleagues. All the time at school, children will be expected to work and co-operate with other children and because they tend to imitate what they see, being great communication role models for them will certainly help them in later life.