I assume that you are asking about the system of primary elections for the presidency in the United States. If so, there are a number of benefits that some people think would be experienced if the country were to have the primaries happen on just one day. Let us look at two of them.
First, voters in all states would be more likely to participate. If the primary is happening on just one day, like the general election happens, people would be more likely to pay attention. The primary would be a big deal and everyone would be aware of it. There would not be any states that voted late in the season after the issue was already decided. That means people in all states could feel that their vote was going to matter.
Second, by compressing the primary system, we would do away with the current system in which states like Iowa and New Hampshire have a disproportionate impact on the election. It is arguably very bad to have a system in which the voters of such small states can have so much of a say in determining which candidates get to continue in the election.
While many people would argue that we should keep our present system, these are some arguments in favor of moving to a one-day primary.