The primary market for securities is their initial issue: the sale of securities by issuers to investors as opposed to trading by investors in the secondary market.
The most common primary market mechanism is an IPO. Any new issue of securities to investors takes place in a primary market so placings and offers for sale are part of the primary market.
Much of the primary market is intermediated by underwriters who relieve the issuer of the risk of the issue failing.
Primary market activities, both underwriting and advising issuers, is, like mergers and acquisitions, an extremely profitable business for investment banks.