nordwärts
northward
Describes movement or direction toward the north.
Die Wandergruppe zog von der Hütte aus weiter nordwärts.
The hiking group moved on northward from the hut.

northward
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northward
Describes movement or direction toward the north.
Die Wandergruppe zog von der Hütte aus weiter nordwärts.
The hiking group moved on northward from the hut.

The ending '-wärts' is very useful and always means 'in the direction of'. You can combine it with all compass directions: nordwärts (northward), südwärts (southward), ostwärts (eastward), and westwärts (westward).
Die Vögel fliegen im Herbst südwärts in wärmere Gebiete.
In autumn, the birds fly southward to warmer regions.
As an adverb of direction, 'nordwärts' (northward) answers the question 'Wohin?' (Where to?). It typically comes after the conjugated verb and describes the direction of a movement.
Nach der Pause fuhren wir mit dem Auto weiter nordwärts.
After the break, we continued driving northward by car.
'Nordwärts' (northward) is almost always used with verbs of movement. Typical verbs are 'gehen' (to go), 'fahren' (to drive/travel), 'ziehen' (to move on), 'blicken' (to look), or 'reisen' (to travel).
Vom Berggipfel blickten wir nordwärts über das weite Tal.
From the mountain peak, we looked northward over the wide valley.
north
'der Norden' and 'nordwärts' both refer to the north, but they do not express the same thing. 'der Norden' is a noun and names a direction or a northern area. 'nordwärts' is an adverb and describes movement or direction toward the north. So you can say 'im Norden wohnen' (to live in the north), but you 'fährt nordwärts' (drive northward). Learners may confuse the words because both refer to a direction. The simple difference is: 'der Norden' is a place or area, while 'nordwärts' describes where something is moving.

Nach der Grenze fuhren sie weiter nordwärts.
After the border, they continued northward.
Am Wochenende erzählte Noah viel vom Norden und von seiner Reise ans Meer.
At the weekend, Noah talked a lot about the north and about his trip to the sea.