Why does a neuron choose to connect to another?
Donald Hebb originally formulated what would later come to be known as spike-time dependent plasticity by famously stating "neurons that fire together wire together". In actuality, the firing has to be sequential (not simultaneous) and causal: if a neuron A fires and causes B to consequently fire, the synaptic strength between them increases. This is how the brain implements learning and memory. [1] This principle fits with the idea that the brain essentially learns causal relationships that exist in the world, as formalized in the Bayesian brain hypothesis [2]. 

[1] Markram et al., "A history of spike-timing-dependent plasticity": http://infoscience.epfl.ch/record/168812/files/fnsyn-03-00004.pdf

[2] Clark et al., "Whatever next? Predictive brains, situated agents, and the future of cognitive science": http://www.fil.ion.ucl.ac.uk/~karl/Whatever%20next.pdf