Hugely means very, or very much. It makes a quality or a feeling bigger: hugely popular, hugely important, hugely successful. It comes from huge, so the picture is “to a huge degree,” but in real talk it is just a strong “very” — people say it even when nothing is actually large. It is common and sits comfortably in speech and in magazines. It does not usually sit in front of a noun by itself (you do not say “a hugely house”). It modifies adjectives, and sometimes verbs: “It helped hugely.”