Each electrode receives signals from a combination of various neural and non-neural sources, such as eye movements, muscle movements, blinks, and noise from electrical wires. The farther a source is from an electrode, the less of that signal the electrode picks up.
Note that the electrode closest to a source picks up a signal that closely resembles the actual source signal. The electrode in the middle of the two sources picks up a combination of the two sources.
ICA takes the signals received by the electrodes and decomposes them into the individual components. The number of electrodes will be the number of components ICA returns.
Now it is possible to mark and remove non-neural components. The program then adjusts each electrode’s waveform to not include these bad components.
Now read:
The introduction of A practical guide to the selection of independent components of the electroencephalogram for artifact correction.
For more info on ICA:
ICA for Dummies – http://sccn.ucsd.edu/~arno/indexica.html
An example of ICA using sound sources – http://research.ics.aalto.fi/ica/cocktail/cocktail_en.cgi
For a lot of detail on the ICA algorithm – http://www.stat.ucla.edu/~yuille/courses/Stat161-261-Spring14/HyvO00-icatut.pdf
References
Figure 1. Robert Oostenveld. The Donders Institute for Brain, Cognition and Behaviour. https://www.youtube.com/watch?v=zOxCqcYmIfA