Here's an attempt to give a very simple explanation.
The asset system is based on "colored coins". That means
that an amount of coin is assigned with a "color marker" that distinguishes
it from "unmarked/colored" coins. It appears as a special coin amount
to a color-enabled wallet.
Now you can link that color marker to a resource, say a contract on web that
says that "I will redeem these colored coins for X amount of Bitcredits after date Y".
The marked coins are thus linked to a future promise of some kind, and so they
become a true asset that can be transferred and traded. See https://www.coinprism.com/
for examples that use the same asset protocol.
This is the most primitive use of colored coins, actually there is no end to their
uses. It is the gateway to 2.0 cryptocoins. All kinds of smart contracts are in theory possible.
Unfortunately there are only few guides and tutorials available and many of them short, dense and
technical. Perhaps this community will popularize their use and bring it to the
masses?