Superfluous or redundant words are words that add nothing but clutter to a sentence or paragraph. Sometimes they are a result of sloppy thinking: for example 'It is thus that we see that it is ...' instead of 'Thus we see ...' Sometimes they are simply the same thought repeated in different ways.
Clutter: 'What is ignored in all the debate about Athenian identity is' or 'What is meant by this theory is'
is much better expressed as: 'Ignored in the debate about Athenian identity is' or 'This theory shows ...'.
Repetition: Every sentence should express a new thought and not repeat itself: 'This shows that despite being at war, the Athenians still regarded the proliferation of the political space within Athens as highly important, so they kept building, because political spaces were thought to be a good thing for Athens, though the war did, to some extent, curtail building operations.' The second half of this sentences is superfluous.
Checking your work for superfluous words or phrases is time well spent, since repetitions and clutter distract attention from the point you are trying to make. Often, superfluous words can just be removed. Sometimes you will need to rewrite.
Just an aside: anybody thinking of writing articles for journals or newspapers needs to be particularly good at weeding out superfluous words. Editors don't appreciate them and if you don't take them out, a sub-editor will be let loose on your piece, with unpredictable results.