So Fuin is an art that as you said, deals mainly on sealing something. However, there are more aspect to fuinjutau nowadays even though everything border down to sealing.
Fuuinjutsu is made up of 6 parts :
The Object/Target of the Seal - basically, whatever you're going to seal. And in this its crucial to understand the latus sense of what it means to seal something. You are able to seal not only a physical object but also energy or even metaphysical events such as souls or chakra. You can also seal links, such as those of a contract summoner with his summon or other seals. You can seal movement but also memories or emotions. The broad range of sealing objects is enormous.
The Medium/Vessel - basically, its what's going to contain the Object/Target. You can have organic vessels, inanimate or even simply pure chakra/energy as a vessel. Some seals are, themselves, a the medium and the vessel.
The Trigger - not all seals have this but 90% of them have. Its what triggers the sealing technique. It can be anything from trying to speak of a secret to simple handseals or chakra. The trigger is always there in latent seals; time delayed seals such as danzo's juuinjutsu. Some however don't have it such as the Contract Seal.
The Binding - this is the seal itself and it can be handseals, kanji formulas, etc. Its basically what will wrap, manipulate and contain the Object/Target into the vessel but also what alters the vessel to allow it to serve as a medium for the target of the seal. Its the most complex part and one of the more important ones.
Chakra - all seals require chakra to be produced, maintained or released. Chakra is what you expend to forcefully seal your target. This means that you'll always need to, as well, spend chakra to keep the target sealed. Some seals, such as the jinchuriki seals, don't use your own chakra (the one from the sealer) but that of the vessel, to keep the target sealed. Vessels can fuel the seals put on them if they are sentient beings and as such with their own chakra source. Because chakra is needed to keep the sealing, it has been verified that seals can also weaken with time as it deplets the chakra used to sustain it or as the vessel or binding becomes weaker/altered.
and
The Key - again, not all seals have this but most do. Its the key to unlock the seal and release whatever is sealed back into the world. A key can be anything from a sequence of handseals, which is more usual, to dna, like blood, or even a simple mental command. The key will basically do the inverse that the trigger does. It will manipulate the bindings into releasing the Target of the Seal.
Also yes I meant those you've seen it use it in the anime and what you saw, but never mind, I'll point them out when we get to individual techniques.
Any question?