I will assume that you are using the term "primary market" in the most common sense of the sale of new securities (debt or equity) to obtain financing. This covers the initial sale of stocks, bonds sold by governments, etc.; secondary markets being the resale of such securities by other parties, although the actual marketplace is typically the same one so it gets fuzzy.
One benefit is the creation of money in equities. Buying of equities values them, and other shares are, by our conventions, valued at the last sale price. This expands the money supply commensurate with the value the public market places on the real economy goods and services.
Looking at your background, this may be more basic than you were looking for...
Advantages with Primary Markets: The seller has complete control on pricing and shortens the value chain, Low Cost as buying products at primary market is less costly as marketers need not travel over a long distance to be involved, Fresh and quality product at primary markets depending on the type of products, Sellers get direct feedback from their client, Primary markets provide easy outlets for producers and encourage job creation.