Tourabu (とうらぶ) - Abbreviation of Touken Ranbu. (Also literally means "sword love")
Touken Danshi (刀剣男士, lit. "sword men") - Touken (刀剣) refers to nihontou (Japanese-style single-edged curved blades) and tsurugi/ken, which are an older style of double-edged sword smithed in China and brought to Japan before the Heian period. Danshi (男士) means 'men', but is pronounced the same as 男子, which means 'boys'. Taking both of these parts into account, touken danshi can be interpreted to mean any kind of male sword.
Toudan (刀男) - Abbreviation of Touken Danshi.
Saniwa (審神者) - Refers to us players, who have traveled to the past to change history. Saniwa can be loosely translated as simply "sage". In the Shinto religion, saniwa are specialized priests/folklorists tasked with the identification of the gods. More details can be found here.
Secretary (近侍) - Refers to the commander of the first unit. Also stands in the inner citadel when you are not doing anything. In battle, he receives 1.5x experience points (3x if he gets MVP).
Inner Citadel (本丸) - This is the main screen. Your secretary will appear in the middle, and if you wait a long time or click on him, he will speak. You can buy new backgrounds for your citadel using koban (小判).
Sakura Fubuki (桜吹雪) - Refers to a state when a sword is in high spirits, with low Fatigue levels. His status will show sakura petals flying in the foreground (sakura fubuki means something like cherry blossom tempest when a lot of petals are scattering the wind). In addition, this status will increase battle capabilities, such as speed, by a moderate amount. See Fatigue for more information about achieving Sakura Fubuki.
MVP (誉) - The MVP badge is given to one sword each battle, usually the one who deals the most damage. In the exp screen, a 誉 badge will appear by him and he will receive double experience points. In addition, he will say a line and his battle sprite will appear on the screen before you move on to the next battle.
Ikkiuchi (一騎打ち) - An in-battle event that has a chance of being triggered when your swords are pushed into a disadvantageous attack formation. When this happens, the captains of the teams will face off and have a decisive battle that could turn the tide of the battle. However, if you lose the ikkiuchi, it does not necessarily mean that the whole battle is lost. See Combat Mechanism for more information about Ikkiuchi.
Toku (特) - An upgrade that occurs automatically when a sword reaches a certain level. See Upgrades.
Kiwame (極) - A further upgraded state that requires materials, an eligible sword, and 96 hours of training. See Upgrades.