There are several types of hostels nowadays, and all of them tend to have their special characteristics; some are more like standard hotels, some are a completely different experience. The main difference is that most hostels offer accommodation in dormitories, or shared rooms. Dorms can be bigger or smaller, can be for males/females only or mixed, but anyway this means that you can share your room with strangers.
Although many hostels now provide private rooms with en-suite facilities, the atmosphere is still very different from that of your average hotel. Whereas hotels only tend to just provide their customers a comfortable place where to spend the night, hostels tend to have more of a social atmosphere which often is derived from sharing dining tables, washing machines, dryers, and much more with with other guests.
Many hostels organize parties and excursions for their guests, and many have a bar where people can meet and get to know each other. In a hostel it is much more likely to start a conversation with a fellow traveller or to be asked for advice, tips and information by someone you have never met before.
Basically, hostels are generally a good place to make friends, to meet people from far away countries with ways different than your own, to exchange tips on clubs, museums, shows, shopping and the like.