In the course of your FMRI studies, you may have at one point stumbled upon the nightmarish world of Independent Components Analysis (ICA), an intimidating-sounding technique often used by people who know far more than I do. Nevertheless, let us meditate upon it and see what manner of things we have here.
Components are simpler building blocks of a more complex signal. For example, in music, the soundwave profiles of chords can appear very complex; yet a Fourier analysis can filter it back into its constituent parts - simpler sine waves associated with each note that, combined together, create the chord's waveform.
A similar process happens when ICA is applied to neuroimaging data. Data which comes right off the scanner is horribly messy, a festering welter of voxels and timecourses that any right man would run away from as though his very life depended upon it. To make this more comprehensible, however, ICA can decompose it into more meaningful components, each one explaining some amount of the variance of the overall signal.
Note also that we talk of spatial and temporal components, which will be extracted from each other; this may seem somewhat odd, as the two are inseparable in a typical FMRI dataset: each voxel (the spatial component) has a timecourse (the temporal component). However, ICA splits these apart and recombines them, in descending order, into components that explain the amount of variance of the original spatio-temporal maps. This is what is represented in the figures shown on the FSL website, reprinted below:
After these components have been extracted, something happens that some (like me) consider terrifying: You need to identify the components yourself, assigning each one to whatever condition seems most reasonable. Does that one look like a component related to visual processing? Then call it the visual component. Does that one look like a resting-state network? Then call it a resting-state network component. This may all seem rather cavalier, especially considering that you are the one making the judgments. Seriously; just think about that for a moment. Think about what you've done today.
In any case, that is a brief overview of ICA. To be fair, there are more rigorous ways of classifying what components actually represent - such as creating templates for connectivity networks or activation patterns and calculating the amount of fit between that and your component - but to be honest, you probably don't have the motivation to go through all of that. And by you, I mean me.
Next we will work through the example datasets on FSL's website, discussing such problems as over- and under-fitting, the Melodic GUI, and what options need to be changed; followed by using ICA to analyze resting-state data.