Iaijutsu and iaido are components of kenjutsu 剣術, the arts of the sword. Iaijutsu, iaido are specific techniques used to draw the sword from the saya (sheath). It is also called battōdō or battōjutsu抜刀術.
The suffix of jutsu 術 means techniques or the art of. Batsu 抜 or nuku means to pull. Battōjutsu means the art of pulling out the sword.
Iaijutsu, on the other hand, has a different connotation than battōjutsu. Iai 居合 is made up of two characters, the first I 居. This character means to be or exist and also has a broader meaning of sitting. The second character, ai 合 means to meet or unite or join.
There is no direct translation into English of Iai. The art of using the sword in everyday situations is probably the best way to think of it. Iaijutsu does not mean the seated forms solely. There is also standing, which is called tachi-iaijutsu 立居合術.
No single person can claim the creator of iaijutsu. Although bushi such as Iizasa Choisai Ienao of Tenshin Shōden Katori Sintō-ryū (14th Century) and Hayashizaki Jinsuke Shigenobu of Shin Musō Hayashizaki Ryū (16th Century) significantly contributed to its spread and popularity within koryū.
Iaijutsu and iaidō are done from various postures from seated to standing. Although the character 居 has the older meaning of sitting, iaijutsu contains the feeling of being at "rest" in a non-battlefield situation and is more relating to that of everyday life. Sitting in a meeting, or having a meal or being served tea, etc. etc. Walking down the street is a part of this "existing in everyday life" idea.
Iaijutsu is concerned with the art of using the sword from its rested position in the saya. The person studying iaijutsu learns to deploy the sword for somewhat defensive purposes. In Japanese swordsmanship, these defensive techniques also include acts of getting the sword out to attack as well. Iaijutsu is not purely defensive action. Methods for stealthy or covert attacks are also included in many systems of iaijutsu and iaido.
In general, the sword is worn through the obi (belt) with the cutting edge facing up and starting around the sixteenth century the sword was easily worn through the belt and hakama since many more samurai were not in dressed in armor. The sword placed in the obi and straps of the hakama became usage. Earlier the sword was worn in a method known as tachi. It with the cutting edge facing downwards. It was suspended by two cords affixed to the saya. It hung much lower than the more modern version of it being in the obi. Having the cutting edge face down in tachi style also puts the handle at a convenient level to draw the sword. Wearing the sword in the obi with the cutting edge facing downwards creates an awkward method of drawing.
The swords (tachi) had also changed more into the katana we know today. The advent of a change in political climate, wardrobe, and utensils such as the uchigatana and katana paved the way for the advent of iaijutsu. The samurai needed a method to use the sword in a different environment.
Iaijutsu and iaido are done from crouched (iaigoshi), kneeling or semi-sitting (tatehiza), formal sitting (seiza), regular sitting (agura) and standing (tachi) postures. The sword might be in the obi, or it might be on the floor to either side of the practitioner. It might also be done carrying the sword in one hand. There is a myriad of ways different schools approach the art iaijutsu in swordsmanship. The handle (tsuka) and sheath (saya) and sword guard (tsuba) are also used as weapons in some schools in their iaijutsu techniques (waza). Iaijutsu can also contain grappling within its techniques. It is not uncommon to use a kick or a punch or joint locks within the iaijutsu techniques.