What is Litecoin?
Litecoin is the result of some of the bitcoin community who joined together on IRC in an effort to create a real alternative currency similar to Bitcoin. They wanted to make a cryptocoin that is considered silver to Bitcoin's gold (see criticism).
Litecoin aims to maintain the unique traits and attributes of Bitcoin, while adding to the mixture GPU-resistant mining and a 2.5 minute block rate. This means that Litecoin doesn't have reason to compete with Bitcoin for the used up computational cycles of your graphics card, but can work independently on your processor.
Differences from Bitcoin
Litecoin had two blocks premined, one more than the minimum single genesis block needed to start a block chain.
Scrypt Proof of Work
Litecoin uses Scrypt as a proof-of-work scheme. Scrypt adds memory-intensive algorithms to reduce the efficiency of GPUs down to the level of CPUs. This greatly limits the ability of commodity hardware to mine at high rates, making it easier for big corporations and governments to obtain a monopoly over mining.
Faster, Smaller Block Chain
The Litecoin blockchain differs from its Bitcoin counterpart in that it tries to have smaller blocks, and generate them four times as fast as the Bitcoin network allows. This means that 1-confirmation (low value) merchants get faster confirmations for their online products, but increases the network overhead.
Miners generate 50 coins per block, like Bitcoin. In light of faster blocks, to properly mimic Bitcoin's generation trajectory, the amount of coins generated gets halved every 840,000 blocks. As a result, Litecoin is scheduled to produce roughly 4 times as many coins as Bitcoin, about 82 million litecoins.
Litecoin does not provide anything significant that Bitcoin does not already provide. Because of this, and Bitcoins much greater size, it is unlikely to gain any significant momentum.
Not Silver to Gold
Litecoin cannot be "silver to bitcoin's gold", because Bitcoin itself is both gold and silver: While in the long-run, the BTC unit may be too valuable for everyday trade ("gold"), there are other, much smaller units that can just as well serve the purpose of "silver" while being naturally/automatically "converted" to/from BTC.
Vulnerability to mining monopoly
Because Litecoin has replaced the SHA256 proof-of-work with scrypt, it is more vulnerable to attack from rich entities (on the scale of big corporations and governments). If Litecoin were to ever become popular, such an attack is inevitable and would negate the benefits of it being a crypto-currency.
Since the aforementioned reasons mean Litecoin has no future potential, it effectively functions as a pyramid scheme, rewarding those who get in sooner at the expense of those who adopt it just before it finally fails (and are left with nothing). This is not the case for Bitcoin, since it has significant potential to become a long-term currency and continually be beneficial to adopters no matter when they begin using it.