Most of us work in teams with a common manager. In our performance reviews, teamwork is usually evaluated, and management literature lauds teamwork and constantly provides advice on how to improve it. Sometimes it seems teams are just little blobs of people, floating through the workplace. But teams don't work that way. At the foundation, they're made up of individuals. Yes, they're working on a common goal, but really it's not one team working on the goal, it's five or seven or nine individuals, and success depends on each one's performance.
Individual Work Roles
In my only sports analogy, teams have positions. In work teams, individuals do certain roles -- you work on this project, you work on that project. Those roles get filled by people who do best in those roles. It's not like everyone works on everything all at once. That's not efficient.
Individual Social Roles
Business is social. So are teams. If everyone on the team is a high motivator, we'll all be motivated but won't get much done. If everyone is a great organizer, we'll have great organization, but won't get much done. This balance of social roles on a team is a great individual contribution.
Individual Specialized Expertise
Think about the last time you ran into a problem with your work. You needed to talk to someone about it. Who, on your team, was it? Why did you pick that particular person? Outside of routine questions that anyone can answer, you'd pick someone who knows a lot more about the problem than you do. People usually engage in parts of the job because it is more interesting to them and they want to learn more about it. Some people in project management, for example, are really into how the finances flow (scary, I know). Others know about how work is planned out. Others know about the relationships on a project -- all specializations.
The Most Important Individual Contribution Is...
...ensuring your team can count on you to do your work. Think about your own work team. Is someone a slacker? Or never finishes their work on time? Or really doesn't get how to do something? Or is utterly annoying? People on the rest of the team have to cover for that person -- taking valuable time from their own work. Or, they have to deal with a level of, well, that stuff as part of what they tolerate on the job. In other words, people who don't do their job bring the team down. Fitting into a team, then, isn't about joining a blob and doing work. One of your priorities is to find your unique contribution, and then delivering so your team can count on you, the Individual. That's the "I" in team.