der Nordosten
northeast
The compass direction that lies exactly between north and east.
Der Kompass zeigt nach Nordosten.
The compass points northeast.

northeast
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northeast
The compass direction that lies exactly between north and east.
Der Kompass zeigt nach Nordosten.
The compass points northeast.

'Nordosten' (northeast) is simply formed from the two compass directions 'Nord' (north) and 'Osten' (east). This pattern applies to all intermediate compass directions, such as 'Südwesten' (southwest) or 'Südosten' (southeast).
Die Vögel fliegen im Herbst Richtung Südwesten.
The birds fly southwest in the fall.
The preposition indicates the function. 'Nach Nordosten' (to the northeast) describes movement in that direction, while 'im Nordosten' (in the northeast) describes a fixed location.
Wir fahren morgen nach Nordosten an die Küste.
We're driving northeast to the coast tomorrow.
To describe the northeastern part of an area, you use the structure 'im Nordosten von [Land]' (in the northeast of [country]) or the genitive 'im Nordosten [Landes]' (in the northeast of [country]).
Die Strände im Nordosten Brasiliens sind wunderschön.
The beaches in the northeast of Brazil are beautiful.
east
'der Osten' and 'der Nordosten' both describe a direction or a part of an area. The difference is how precise they are. 'der Osten' means the direction in which the sun rises, or the eastern part in general. 'der Nordosten' lies between north and east, so it is more precise. The words are easy to confuse because 'Nordosten' also contains 'Osten'. If all you need to say is that something is located to the east, 'der Osten' is enough. If it is also farther north, 'der Nordosten' is more precise.

Im Nordosten des Landes bleibt es am Montag trocken.
In the northeast of the country, it will stay dry on Monday.
Der Wind kommt heute aus dem Osten.
The wind is coming from the east today.