This phrase helps to highlight how individual actions have to be concurrent with the collective entity. The metaphor of teamwork is often employed to bring about a sense of ethical conduct that ensures that individual action is consistent with collective aims. It helps to provide guidance to individuals who might feel that individual actions should trump all. In this light being able to stress that "team commitment is essential" helps to drive home the point that all individuals are bound to a team concept, an entity that is larger than oneself. In this light, individual success and collective striving are one in the same.
"Commitment to a team is essential" sound like the kind of thing you'd see in an advertisement for a job opening. It would help if you gave some context for where you found the phrase.
Literally, it is stating that in order to be a part of the team you must be committed to that team. As the old saying goes, "a team is only as strong as its weakest link." Unless all members are committed to the team those members will act in ways that are in there individual best interest rather than what is in the interest of the group. Imagine, for example, if you are part of the basketball team and half the guys (or girls) don't show up for a game because there's a party going on that night...they would not be committed to the team and it would fail. Now imagine that everyone showed up to all the practices and games even when it wasn't convenient for them. That shows real commitment and increases the chances of success.