User Issued Asset is an asset that anyone can create and trade on the Bitshares network. There are UIA's representing a company, and others representing another cryptocurrency. UIA's created by openledger start with "open.", and are cryptocurrencies backed by ones held in custody by openledger. They are essentially the same as "poloniex bitcoins", which are "poloniex issued assets" on the poloniex centralized system.
Market Pegged Assets are a different beast. They are assets that follow the market value of any currency or commodity. They are backed by 2.5x the amount in BTS, ensured by a smart contract. They follow the market price quite closely, because of inbuilt incentive systems. An example is bitUSD, which is created in the Bitshares network, and follows the value of USD.