Trading by non exchange-member brokers/dealers and institutional investors of exchange-listed stocks. In other words, the third market involves exchange-listed securities that are being traded over-the-counter between brokers/dealers and large institutional investors.
Taobiz explains Third Market
Before selling an exchange-listed security to a nonmember, a member firm must fill all limit orders on the specialist's book at the same price or higher. Typical institutional investors who take part in the third market include investment firms and pension plans.