Spuriousmonkey is right, during the early stages of development, the brain, through the mechanisms of neurotrophic factors, makes an enormous number of connections, many of which are useless and therefore eliminate themselves. This is, however a more complicated process that would take a while to explain. As adults, the neurons that are in place pretty much stay in place and there is not too much new growth. The memories that you have are not stored in neurons, but in the connections between neurons. When neurons are activated in certain patterns, their connections grow stronger. One might think of it as a multilateral telegraph whose signal becomes stronger when the message is repeated. This is called long-term potentiation--neurons are more prone to 'fire' when the pathway is activated. Your brain is a series of 'telegraph' lines. Here's the interesting part: multiple signals do overlap and can be distinguished in a relatively simple manner by the brain. This is likened to a Fourier transform, a mathematical operation in which complex wave patterns are broken down (deconvoluted) into their individual frequencies. So, neurons can be used for many memories at once. The reverse process can also occur. If a certain frequency of pulses is administered (by experiment or naturally), a process occurs that is called long-term depression. The connection will not be easily activated again. Taking into consideration all of these possible operations, it becomes easier to see how so many complex memories can be formed.