Fuuinjutsu is quite simply storage. However, utilising the properties of Fuuinjutsu, you are able to seal people, places, chakra, and even intangible elements like fire and lightning. These objects are then sealed within an object that we commonly refer to as a 'vessel'.
Using Fuuinjutsu, we are able, to some extent, violate fundamental laws which govern the physical plane of existence. For instance, when an object is sealed it does not really exist in the same space as other objects. It is sort of stuck into its own space, and since we've never experienced what it looks like inside a seal we can only theorize. However, when Naruto visited Kurama we did get a glimpse of the inside of a seal. Using Fuuin, you can literally expand the personal space of an object in order to accommodate multiple objects.
A seal itself is like a dish with 6 main ingredients that come together to form it. The main object which is being sealed, the vessel it is sealed in, a trigger which initiates the seal, the object used to bind the target, chakra used to fuel the seal, and finally a key to release the seal. It sounds more complex than it really is. In practice, most of these are relatively simple.
Then, we move onto practical applications of seals. By sealing weapons, they can be more easily and quickly accessed during battle. For example, it'd be simpler to tap my wrist to summon a sword, than to draw it from my side. This can add an element of surprise to your battles, making it difficult for someone to react. You can also seal bodies, for easy storage after killing an opponent. You can seal incoming techniques, you can seal explosions and release them as the opponent nears, you can seal skills of the opponent, his chakra, limbs, etc. The possibilities are almost endless.
Questions?