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I often here the word "node" being used in the context of parallel programming. For example from the following web-page I have the line

All the compute nodes on all the the clusters at the CUNY HPC Center include at least 2 sockets and multiple cores. Some have 4 (ATHENA), some have 8 (ZEUS, BOB, ANDY), and some have 16 (SALK). These multicore SMP compute nodes offer the CUNY HPC Center user community the option of creating parallel programs using the OpenMP Symmetric Multi-Processing (SMP) parallel programming model.

Now what does a compute node mean here? Does it mean a single desktop computer? Meaning the ATHENA cluster has 4 desktop computers joined together ZEUS, BOB, ANDY 8 and SALK 6?

Or does it refer to a single Intel CPU? Please clarify.

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Its a single "system" in a cluster of many systems. This could be a classical desktop or server system, a VM (though its unlikely, its possible),a blade in a blade server arrangement, or a single repeating unit in a supercomputer such as this one from a blue gene. Each node runs its own instance of an operating system, and is connected to the cluster via fast network connections.

The article contradicts itself in a few places but as i understand it from the part that lays out the system specifications, athena consists of 86 compute nodes (each apparently a 1U server) and one 'head node' that controls it, each of which is a dell poweredge 1850. Likewise for each of the other systems.

The wikipedia article on computer clusters goes into this in some detail

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