
abseits
away from
Used as a preposition with the genitive to express spatial distance or separation from something.
Wir machten ein Picknick abseits der lauten Straße.
We had a picnic away from the noisy road.
offside / away
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away from
Used as a preposition with the genitive to express spatial distance or separation from something.
Wir machten ein Picknick abseits der lauten Straße.
We had a picnic away from the noisy road.

off to the side
Used as an adverb to express that someone or something is not directly involved in the main action or is located in a distant place.
Während alle diskutierten, stand er nur abseits und schwieg.
While everyone was discussing, he just stood off to the side and remained silent.
The word 'abseits' (away from/off to the side) derives from 'ab' (away) and 'Seite' (side). So it literally describes a position that is away from the side or from the center.
Das Haus liegt etwas abseits, mitten im Wald.
The house is located somewhat out of the way, in the middle of the forest.
'Abseits' (away from/off to the side) can be used as a preposition with a noun or as a stand-alone adverb. As a preposition, it introduces a location; as an adverb, it describes a position without a direct object.
Wir saßen abseits des Trubels auf einer Parkbank.
We sat on a park bench away from the hustle and bustle.
When 'abseits' (away from) is used as a preposition, it requires the genitive. In colloquial speech, the dative with 'von' is sometimes used incorrectly, but in written language the genitive is correct.
Ihr Ferienhaus liegt abseits der großen Touristenorte.
Their holiday home is located away from the major tourist resorts.
outside / outside of
Außerhalb and abseits can both describe a location beyond a place. Außerhalb merely states the position beyond its boundary. Abseits additionally emphasizes that something is away from the place or the usual activity and lies in a more secluded location.

Das neue Haus steht abseits des Dorfes an einem einsamen Waldweg.
The new house stands away from the village on a lonely forest path.
Das neue Haus steht direkt außerhalb des Dorfes.
The new house stands just outside the village.