In the world of Naruto, a jutsu ("Technique" or "Skill" in Japanese) is a general term referring to any technique a ninja might use that not any ordinary human could naturally imitate. In some cases the line between a simple action and a Jutsu is blurred and vague, allowing for some humor (Uzumaki Naruto: "What? How did you get loose?!" Uchiha Sasuke: "Rope Untying no Jutsu. It's basic stuff.")
Jutsu are usually the product of channeling chakra to a certain part or parts of the body (through the inner coil system, which is to chakra as blood vessels are to blood) and then manipulating it to create an effect which wouldn't be possible otherwise. If the inner coil system malfunctions or is blocked in any way, it is impossible to perform any jutsu at all.
The English version of the Naruto manga has English names for the attacks, which are often stated with the attacks' Japanese names in translations starting in 2005. The North American Naruto fanbase prefers to use the Japanese as of April 2005. In the English TV show, a different set of attack names is used.
Generally speaking, jutsu are divided into three categories: Taijutsu (Body techniques), Genjutsu (Mind techniques) and Ninjutsu (Techniques that rely on sources beyond those). Besides these main categories there is another, more specific category: Fūin jutsu (Sealing techniques).
Besides being either Ninjutsu, Taijutsu or Genjutsu a jutsu can also be "Hiden" ( Secret). Hiden jutsu are jutsu passed down from generation to generation within some clans.
There is technically another category called Kinjutsu (Forbidden Techniques), but it refers not to the type of the jutsu but to the fact that it is forbidden to learn or perform it. A technique can be categorized as kinjutsu if it either causes great harm to the user if overused, such as Rock Lee's Lotus techniques, or if the techniques are dark or sinister in nature, such as many of Orochimaru's skills.
There are also Kekkei genkai. These are not really jutsu, but special, genetically inherited abilities like the ability to copy other jutsu or to merge your body with other bodies. Kekkei genkai abilities that work via the user's eye are called Dojutsu (Pupil Techniques). Some jutsu are based on Kekkei Genkai, like Tsukuyomi.
There are seven different ranks in jutsu:
S-rank: Secret: extreme level jutsu
A-rank: Kinjutsu: ultra high level jutsu
B-rank: Jounin level jutsu
C-rank: Chuunin level jutsu
D-rank: Genin level jutsu
E-rank: Academy student level jutsu
No rank: Jutsu relying on the unique abilities of the users (Kekkei genkai, Hiden jutsu)
Genjutsu (Illusion Techniques) are techniques that use the chakra in the victim's nervous system to create illusions; an advanced intellectual Ninjutsu. The most commonly seen Genjutsu is simple creation of phantasms- causing the targeted person to hear, see, smell, taste and feel things that are not actually there in order to manipulate them; other applications of Genjutsu are rare.
Ninjutsu (Ninja Techniques) is hard to define; it is basically any technique that does not fall under either Taijutsu or Genjutsu, which means that it uses sources outside those naturally available to the body or the mind to accomplish its task. Ninjutsu relies on chakra and, most of the times, hand seals (Sequential positions the hands are put into in order to mold chakra in the necessary manner to perform a jutsu).
Taijutsu (Body techniques), or more figuratively hand-to-hand combat) refers to any techniques involving the martial arts or the optimisation of natural human abilities in general. In some cases chakra is involved to enhance the techniques, but generally speaking a Taijutsu user can fare well without much chakra available compared to a Genjutsu or Ninjutsu user. See also: real-world Taijutsu, basically a general term for a wide range of martial arts techniques.