"Processing" doesn't have a consensus definition in the neuroscience community, but a neuroscientist could, with good justification, use that definition if they had a particular experimental scenario. In this article, Smith, et al., use a more narrow definition based on well-known response in which a neuron is selectively-sensitive to a bar of light at a particular angle. How a neuron becomes selectively-sensitive (i.e., how it fires to that angle and not to all the others) is the "processing".
It is overly simplified to say that for the processing to be useful that it has to share the result. If a particular part of the dendritic sub-tree was stimulated enough, it could bring the neuron into a particular electrophysiological state that succeeding synaptic input would cause a wholly different computation to occur. Thus, you can see the importance of timing discussed by the sister comment.
It is overly simplified to say that for the processing to be useful that it has to share the result. If a particular part of the dendritic sub-tree was stimulated enough, it could bring the neuron into a particular electrophysiological state that succeeding synaptic input would cause a wholly different computation to occur. Thus, you can see the importance of timing discussed by the sister comment.