This a great question, but one that will have many opinions. I would say that the voter registration campaign was one of the main reason for progress, but not the main. In a complex movement to speak of the "main" is not an easy task.
There were many important developments during this time period, such as the integration of blacks in universities, the Birmingham campaign of 1963, which sought the desegregation of Birmingham's downtown merchants, and the 1963 march on Washington. All of these were important, not to mention the freedom rides. Having said this, let me briefly mention what the voter registration campaign sought to do.
The voter registration campaign was an important step in the civil rights movement as it sought to give the right to vote to all blacks. This campaign was resisted greatly by many whites in places like Mississippi. The 1890 constitution of Mississippi made it very difficult for blacks to vote on account of it requirement, such as poll tax, residency requirements, and literary tests. Despite these obstacles, the voter registration campaign was successful and brought the issue to the fore of the civil rights movement.