It has deceptively superficial similarities with English and German. It's closer to the Scandinavian languages, but it's much more complex than any of them.
Like German, Icelandic has three genders and four cases, but it inflects its nouns and adjectives more extensively than German, and much more than the Scandinavians. The adjectives have strong and weak forms.
The verbs are often highly irregular, and in addition to active and passive have an additional voice, the middle. The middle voice in Icelandic is difficult for an English speaker. In English, as I understand it, the verb in a sentence like 'fire broke out' or 'the works began' is considered to be the middle voice. It's the same if you translate those sentences into Icelandic: 'eldur braust út', 'framkvæmdir hófust'. But apart from conjugating differently from the active voice, a verb in the middle voice in Icelandic sometimes translates as passive, sometimes translates as a reflexive, and sometimes has an entirely different meaning: 'koma' - come, 'komast' - make it, progress. Often you just have to memorise how it is used in a given situation.
Icelandic revels in impersonal constructions which have no real cognates in English or German, or in the Scandinavian languages for that matter. It also has 'quirky subjects' where the apparent subject is in the dative or the accusative: 'mér finnst..' meaning 'I think' (literally 'to me finds ..') or 'mig vantar' - 'I need', literally 'me needs'.
Many Icelandic verbs have direct objects in the dative rather than the accusative, especially when they involve a sense of force or direct action - eg valda - cause, breyta - change. Not only do you have to remember these verbs, you have to remember when forming the passive to put the subjects in the dative rather than the nominative: 'Vatni var breytt í vín', water was changed into wine, with vatni, water, in the dative, not nominative (vatn).
English is full of bewildering verb compounds, eg 'put up with', but Icelandic leaves it in the shade. These are just some of the difficulties for an English speaker.
On top of all that, the pronunciation is very tricky, and when spoken at speed it is difficult to understand without a great deal of practice. But it is a fascinating language, it has great charm and subtlety, and an amazingly rich literature.