We know more about the early visual cortex than about any other brain area. This is because neurons in the early visual cortex are delightfully predictable. For example, a neuron may respond optimally to a bar of light of a particular width and orientation: If an observer sees such a bar of light, the neuron will start to fire. In order to fully characterize this neuron, all you need to do is systematically try out a lot of different widths and orientations and see which combination works best. This may be a lot of work and requires a highly invasive procedure (i.e., opening up the observer's skull and sticking electrodes into the brain), but it's definitely within the realm of possibility. (If you're interested, you may enjoy the paper by Wurtz (2009), in which he describes the seminal contribution of Hubel and Wiesel to the understanding of the early visual cortex.)
But, of course, researchers want to go beyond the early visual cortex. After all, neurons that “like” titled bars of light don't tell us much about what we really want to know, such as how we are able to recognize things. Unfortunately, it has proven very difficult to characterize more complex neurons. This does not mean that it's difficult to elicit a response from these neurons, not at all. But it's difficult to figure out exactly what it is about a certain stimulus that makes a neuron respond. For example, in a famous study, Quiroga and colleagues (2005 …