Why does a neuron choose to connect to another? I have been reading about neuron creation, guidance cues and all sorts of highly complex mechanisms used to allow one neuron axon to extend or connect - but to what end?

Why does one neuron end up connecting to another? (instead of all the others)
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