You can see that most of the neurons are at most 10 micrometers thick. That's really thin for a human eye to see. As a fun fact, we can see Squid giant axon because they're about a millimetre thick. Here's an image with human hand to scale. read more
It is long so it can connect with other nerve cells from a distance and it is branched so that it can create connections (synapses) with multiple different nerve cells at the same time. read more