Ah, another victim of the nonsense "rule" against infinitive splitting. It gets somewhat clearer if you rewrite both occurrences of "consciously to think" to "to consciously think".
The other part is the "there is something that it's like to" thing, which is kind of a set phrase/idiom in philosophy, meaning "this is a thing that can be experienced". Sentience is often defined that way: there is something, even if you can't describe it any more precisely, that is "this is what it's like to be a human", but not "this is what it's like to be a rock".
(This comment is intended as an explanation of that mess of a sentence, not a defense of it.)
The other part is the "there is something that it's like to" thing, which is kind of a set phrase/idiom in philosophy, meaning "this is a thing that can be experienced". Sentience is often defined that way: there is something, even if you can't describe it any more precisely, that is "this is what it's like to be a human", but not "this is what it's like to be a rock".
(This comment is intended as an explanation of that mess of a sentence, not a defense of it.)