As far as I can tell, morphological analysis is a technique used by Bible students to better understand the original languages in context.
How does one go about using a tool such as Robinson's Morphological Analysis Codes?
Most of the answers so far are getting all hung up over very specific examples of morphological analysis. It is by far better to start with the basic notion of "morphological analysis", then look at how each of these instances already mentioned meet the goals of morphological analysis.
Morphological analysis means exactly what the etymology suggests: it is analysis of the forms of the words used, explaining their grammatical significance. The obvious example is picking a word in the text, such as δεδικαίωται, looking at its form to not only tell what verb it is from (in this case δικαιόω), but how the endings (rarer: prefixes/infixes), modify the basic meaning of the word.
In this case, that means explaining that it is perfect passive indicative third person singular of the verb δικαιόω.
The analysis may or may not include how the general rule for forming the specific form applies in the specific case. So, for example, it may explain that the δε prefix marks the perfect tense, and that the ω in δεδικαίωται is the result of contraction with a standard marker for the third person in secondary tenses, a historical σ being dropped. But this kind of detail is not common for the tools offered by sites like Blueletterbible.org or eSword. Perseus gets close, though.
To really familiarize yourself with what a morphological analysis tool does, I would start with the one at Perseus rather than either Blueletterbible or Robinson's codes. This is because the Perseus tool gives a much more complete analysis, also including the ambiguities that these others have resolved by relying on more than mere morphology. The main drawback to the Perseus engine is that they removed the feature of allowing entry of a form to analyze via Greek keyboard: you now MUST enter it using their Betacode, which I find unpleasant. But it is not that hard to learn.Tweet