In this particular case, there is not any significant difference in meaning, but in other cases there may be.
To say "X is part of Y" means that X is some portion or element of Y, but normally not the whole of Y. For example:
Hydrogen is part of the substance of a star.
To say that "X is a part of Y" means that X is a discrete element or component of Y, often a part in the sense of one of the things to be assembled into Y. For example:
The trigger is a part of a pistol.
When the phrase is being used metaphorically, there is often little or no difference. For example:
- Conflict is part of marriage.
- Conflict is a part of marriage.
The meaning here is the same. Marriage is not a machine to be assembled from different parts, nor a simple mix with various ingredients like a soup, but a complex experience with many aspects, and the speaker is saying in either sentence that conflict is one of those aspects.
The form "a part" emphasizes that the thing referred to is or can be thought of as a unit among other units. So "He was a part of the team." says that he was one of several members of the team.
The form "part of" without "a" emphasizes the idea of being an aspect of or an ingredient of. So "He was part of the team." says that he was in the team, but not the whole of it, and suggests thinking of the team as a unified thing more than the other form.
These differences are subtle, and a casual fluent speaker may pick one form or the other without much considering such implications, and use either form to mean just "he was on the team" with no more detail.