Technically speaking, an altcoin has value for the same reason everything else has value - people are willing to assign that much value to the object.
When I am looking into investing in an altcoin, I personally look into the devs, the community and the technology in that order. Novel tech is always good but it doesn't mean anything if there are sketchy devs or no community to pack it.

The more altcoins are accepted as currency by mainstream vendors (ie. how Bitcoin is accepted at some restaurants, websites such as Overstock, etc) can add value. Also, features and mentions in crypto and mainstream media can aid its perceived legitimacy (even though press coverage alone doesn't necessarily mean it is actually legit/safe/valuable)

There are many factors, especially the price of Bitcoin, the de factor reserve currency of the Bitcoin world, price of the U.S Dollar, Innovation, energy put into securing the blockchain of a coin, and reputation issues such as public perception, scams, and media response. Dilution of the market means many alternative cryptocurrencies will find it hard to gain a foothold. But many have a cult following so have some value. Legal issues can vary the price also as discussed above.