Overview - Chakra, Hand Signs, and the Eight Gates
Jutsu ("technique" or "skill"), are special abilities used by the ninja of the Naruto world that a normal human could not perform. They usually rely on the manipulation of the "chakra" within the human body to execute, the most common method of doing so being through hand seals. Jutsu can be used as attacks, to heal others, seal spirits or areas, and much more.
Hundreds of jutsu have been revealed in the series so far, which have different names depending on the media they are presented in. The English translations do not use the literal translations of the Japanese terms, and there are differences between the anime and manga translations.
By combining body energy created within the cells, and spiritual energy (force of will and mental fortitude), ninja can create chakra, which can be used to perform jutsu, or otherwise manipulated.
Once chakra is created, it moves throughout the body to chakra (release) points through the chakra system, simular to the circulatory system. It can be manipulated through means such as hand signs to create effects going against the laws of nature, for example walking on water, or breathing fire.
There are five basic types of nature manipulation, corresponding with the elements, and an additional Yin Yang manipulation, which alter the quality of chakra. The five elemental types are: Earth, Water, Fire, Wind, and Lightning. Each is strong against the next in line, but weaker than the previous (lightning loops back to Earth). For example, a fire-style attack would be very strong against a wind-based one, but weak against a water-type. Attacks of the same type can also counter each other, depending on their strength.
Nothing is yet known about the Yin Yang form of nature manipulation.
Most ninja have a natural affinity for one of these elements, and will have an easier time learning jutsu of that type. They are still able to learn other elements, but it is more difficult, and more common in higher ranks.
Some kekkei genkai also allow shinobi to mix the basic elements to create new ones. For example, Haku's Hyōton jutsu, mixing Water and Wind into Ice, and the Mokuton jutsu, mixing Earth and Water into Wood.
 The Eight Inner Gates
The Eight Gates are points in the chakra system that limit the overall flow of chakra through the body, in order to prevent it from weakening too quickly. By learning to open these gates, one's own physical limits can be transcended, at the expense of the body. Each gate offers many times the opener's original strength, and also more damage to themselves. By opening the final gate, one will gain enough power to surpass a Kage, but use up all the energy of the body in the process, and subsequently die. This state is called Eight Inner Gates Formation.
 Hand Signs
To be able to use Ninjutsu and Genjutsu, a Shinobi must be able to do hand Seals/signs (special hand movements). These will activate the chakra the right way so the Shinobi can perform the Nin/genjutsu they wish for. Some jutsu need combinations of the hand signs. Lets take Chidori for example. To perform a Chidori the Shinobi must combine the Ox, the Hare, and the Monkey. If the seals are performed wrong then the jutsu will not work. It may even backfire. There are 12 basic Hand signs and they are named after the Chinese Zodiacs. Then there are some special signs that have evolved from these. In the Naruto Series the names of the seals are sometimes shortened.
The Bold Text in the boxes are their full name.