Meito

A Meito (名刀) is not a type of sword but rather the status of a sword.

In Japan, this means the sword has a history and is of legendary status. The blade is normally a quality blade which stands out above all other swords in its endurance and sharpness.

A meito is sometimes associated with the warrior who wields it and becomes part of his identity. Regardless of who owns them a meito is regarded with highest respect in Japan and to be given a meito is to carry a great honour alongside it. Often warriors who lost in battle would have their meito taken from them by the victor, thus losing their honour alongside it as to lose a Meito is to disrespect the honour of wielding it.

To wield a meito honorably, usually it would be passed down to them from master to pupil or from another family member. There exist several other methods alongside this which are acceptable but uncommon. Another method of gaining a meito honourably was to be offered it, this was usually out as show of respect from one person to another. A warrior may also win it in battle against another warrior in a fair duel and thus be allowed to claim it as their own.

To steal a meito or gain it using another dishonorable action is to show the meito disrespect and warriors who do so were often frowned upon. To put the status of a meito in a western style of thinking, a meito to would be considered in status on par with swords like Excalibur (which would be regarded as King Arthur's "meito" in the Japanese sense).

One Piece
In One Piece, meito is often mistranslated as either part of the name of a sword (e.g. Zoro's Shusui which is often recorded by fans as "Meito Shusui" instead of just "Shusui" in error by those who do not understand that Meitou is a status) or as a "named blade" (understandable given that if you break up 名刀 it forms 名 for name and 刀 for sword.) The latter is more accurate but still incorrect as any blade can have a name, but only a few swords are Meito.

Tashigi's dream is to free all the meito from the hands of villains such as pirates. She believes the swords are crying because instead of being used for noble and honorable deeds, they are being used for criminal use. Her reason for tracking Zoro is to gain ownership of his meito, the Wado Ichimonji which she believes is in the hands of a bad person. As of Chapter 541, she has no victories over Zoro in her quest and as far as we know while she has taken the sword Kashū, a sword not listed as a Meitou but is still one of the Ryo Wazamono Grade Swords, she has taken none of the Meito in her journey of Justice.

Meito is translated simply as Famous Sword in the Viz Manga and Legendary Sword in the FUNimation dub.

List of Meito

 * Wado Ichimonji was Kuina's family meito and Zoro was allowed permission to wield it as part of their promise to each other and carry with it her dreams. Zoro tends to keep this sword in his mouth and apply it for his steel cutting techniques besides his frequent use of it in Santōryū situations where he is forced to use one sword. It is the only sword that Zoro has had from the beginning of the series and never got broken.
 * Shigure is Tashigi's meito. Little else is known about this katana, but she seems to be very proficient wielding it.
 * Yubashiri was Ippon-Matsu's family meito, and he gave it to Zoro after seeing him testing the cursed Sandai Kitetsu, knowing the sword would have a better master than staying at the shop. The sword was destroyed by Shu, and is now laying at rest at Thriller Bark.
 * Ryuma's meito was his sword Shusui which belongs to Zoro now. Upon defeat, Brook's zombie offered it to Zoro as a sign of honor for their battle. Another reason why he gave the sword to Zoro was because he shamed the samurai it inhabited by losing to Zoro. Zoro compared it to "a problem child" yet he was able to hold back Oars alone with the blade. This strongly implies that he isn't capable of using its full power yet.

Trivia

 * Though there are many named swords in the One Piece world, many of which fall into the katana grades, only a few of them have been mentioned so far as "meito" when introduced.
 * So far in the series, Zoro has held the most meito to date. In fact the only named sword he owns not mentioned as a meito is Sandai Kitetsu. However, because of the kitetsu curse, swordsman generally avoid the three kitetsu blades. Thus, few swordsmen would be associated with using one.