Shinobi — They are, as stated by Hashirama, "those who endure". The term is interchangeable with ninja, though I believe it's more proper that shinobi is generally ninja part of a village.
Chakra — It is the combination of physical and spiritual energies inside the bodies of everyone. Focusing the chakra in specific ratios can allow users to perform special techniques (Ninjutsu & Genjutsu) as well as enhance their own power (Taijutsu). Chakra was originally stored in the Chakra Fruit of the Shinju Tree, but once it was eaten by Kaguya, it was passed on over the generations. Everybody's chakra is a unique color. Bijuu chakra is shown to be different from normal chakra. There is also Sage Chakra (Senjutsu) that uses nature energy, energy outside, as opposed to normal energy that uses a user's energy.
Ninshu — The original teaching of the Sage of Six Paths. He taught Ninshu as a means of connecting people together and bringing peace by empowering one another.
Ninjutsu — Misguided teachings and result of Ninshu. It is what happened as a result of people using chakra to power themselves instead of coming together.
It should be noted that Ninshu and Ninjutsu are the same, though the only difference is the "teachings". Both revolve around utlizing chakra within oneself. However, Ninshu is like teamwork, and Ninjutsu is solo.
Taijutsu — Body Arts. It's the use of your body in fighting. It's kicking, punching, slapping, etc. Chakra can be used to enhance it's capability, like the Hyuga's Gentle Fist, or Hashirama/Tsunade/Sakura's Chakra Enhanced Strength.
Genjutsu — Illusion Arts. It focuses on casting illusions or false realties by disrupting chakra networks. In nearly all cases, Genjutsu is used on the opponent, disrupting their chakra network and effecting their brain waves to create false settings. Though there is Izanagi, which is a genjutsu cast upon the user. To get out of a Genjutsu, you have to realize you are in one first, and then bring yourself back to reality with pain, or disrupt your chakra network.
Yin-Yang — To be honest, I'm not that clear with this one. I know that it's Physical and Spiritual energies, but I never really understood what it did in the series. I know how Yin is predominantly involved in Genjutsu, or how Yamato said Nara clan's jutsu uses Yin or Yang (can't remember) or how Tayuya's ghost thingies have low physical energy. So I'm gonna need some info on this.
Clans — Not sure how to explain this exactly. Senju, Uchiha, Nara, Uzumaki, Hyuga, Saratobi, etc. It's like, a big family. Clan's generally have some form of recognition. For example, Senju were simply recognized as being extremely powerful (I assume they have a Water affinity cause of Hashi and Tobi, and being stronger than Fire, which is the Uchiha's affinity, but I digress). Uchiha are known for their KG, Sharingan, and their Fire affinity. Hyuga are known for their Dojutsu KG, Byakugan, and the strongest Taijutsu style, Gentle Fist. Uzumaki known for their exceptional Fuin ability and longevity and chakra pool. Nara for being smart and their Hiden Ability, Shadow Techniques, Saratobi are known for Fire usage.
Some clans have KG that are a bloodline limit and is genetics, so it can't be taught (unless you're the 3rd Tsuchikage, who can apparently learn Dust :|)
Some clans have HA that are just secret techniques. They can be learned, but they are considered extremely secretive and only the members of the clan know it.
Nature & Shape Manipulation — Two fundamental manipulations of chakra for Ninjutsu. Nature involves making raw chakra into one of the 5 basic elements (Fire, Wind, Lightning, Earth, and Water). You can combine them if you have a KG to perform advance elements. Elemental chakra is stronger than raw chakra. Shape Manipulation can be done on both raw and elemental chakra. It involves focusing the shape, like making a dragon head, or making a ball of fire. Two most common types of shape manipulation involve rotation and compression into a sharp point/spear like head. Highest form of shape manipulation is Rasengan.