Oh boy this is a far-reaching topic. To answer this briefly, the founder of the Ming, the Hongwu Emperor first imposed the haijin, or maritime prohibition, in 1371, just a few years after he chased the Mongols out of China. Before this time, China has had a great maritime trading tradition, especially during the Southern Song, that extended the Chinese trading network by sea all the way into the Indian Ocean. Hongwu's outward concern in imposing this ban was the Japanese pirates, who raided the coast of Korea and northern China due to the turmoil of their Nanboku-chō period, when the Japanese imperial line was divided into two. Some scholars supposed that there was another reason though, which was to curtail the influence of the sea trading coastal communities, since they could be seen as a threat to the new dynasty's centralization efforts.

Under the prohibition, private sea trading was banned. All maritime trade were to be conducted through the officially sanctioned "tribute trade", which was a kind of trade where foreign states presented tributes to the Chinese court, acknowledging themselves as vassals of the Middle Kingdom, and receiving gifts as a sign of imperial favour. This trade, in addition to being humiliating to the foreigners involved, was clearly inadequate to the demands of the markets, both domestic and foreign, since the Ming had strict rules about how often a "vassal" could come to present tribute (often 5 or 10 year intervals). Hence, from the early years of the haijin, traders turned to smuggling.

When Hongwu died and his son Yongle came to the throne (through a coup against his nephew), Yongle tried to tackle this problem by sending great treasure fleets out to bring the official trade to foreign states, making sure that the foreigners only traded through the official channels. (This is only one of many reasons why Zheng He's famous voyages came to be, I made a post listing those reasons some time ago ) However, these voyages were stopped after Yongle died, and the most effective means of martime trade became smuggling, again.

Troubles with the Japanese pirates subsided after the Ashikaga shogunate consolidated power throughout Japan, but China's sea ban remained in place. Tribute trade with Japan continued up to its Sengoku period, when the hold of the Ashikaga waned and power became divided by the warring regional daimyo. These internecine feuds even reached China in 1523, when traders from the Ouchi clan fought with those of the Hosokawa clan in Ningbo, the designated port of call for Japanese tribute bearers, just so one clan can be recognized as the official Japanese tribute bearer over the other clan! (and benefit from the tribute trade) The brawl got so out of hand that when a Ming fleet appeared onto the scene to restore peace and punish the troublemakers, the fleet itself got defeated and the Japanese traders got away. After this episode, the Ming banned all Japanese from trading in China, who would have to throw in their lot with the pirates on offshore islands in order to trade Chinese goods.

Around this time the Portuguese began to appear in Chinese waters. They sought trade with China, but they didn't make a good impression on the Chinese since they took over Malacca, a Ming tributary. After being chased from Cantonese waters, the Portuguese converged onto the port of Shuangyu, on the Zhoushan Island off Ningbo, where the Japanese traders and the pirates had operated, away from the reach of the Ming navy. These pirates were called "wokou", to continue using the name for the earlier Japanese pirates, but the pirates this time were mostly not Japanese but Chinese traders driven to piracy because of the sea bans. By calling them "wokou", local authorities could disguise the issue and pass the blame (some even benefitted from sponsoring and sheltering the pirates), but the more alert officials realized that the issue was not a foreign affair but a domestic one. The wokou troubles were eventually settled through a combination of military and economic means, and the sea ban was relaxed with the opening of Yuegang (or Moon Harbour, off Zhangzhou, Fujian) for trade in 1567. The ban against trading with Japan was still in place, but this was alleviated by trading ports in a third-party state, like Taiwan and Macau (which was granted to the Portuguese in appreciation for their help against the Cantonese pirates).

Though the sea ban would be tightened and relaxed from time to time after this, the Ming was in decline in the 17th century, and its maritime policies were not well enforced. Militant merchant groups, the successors of the "wokou" pirates, would dominate the seas in this period, continuing past the fall of the Ming dynasty in 1644 until the Manchu Qing conquered Taiwan in 1683.