hinauf
up
Expresses upward movement, from a lower to a higher position, often from the perspective of moving away from the speaker.
Wir sind langsam den steilen Bergpfad hinauf gewandert.
We slowly hiked up the steep mountain path.

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up
Expresses upward movement, from a lower to a higher position, often from the perspective of moving away from the speaker.
Wir sind langsam den steilen Bergpfad hinauf gewandert.
We slowly hiked up the steep mountain path.

The word is made up of 'hin' and 'auf'. 'Hin' describes movement away from the speaker, while 'auf' indicates the upward direction.
Schau mal, wie die Katze den Baum hinauf klettert!
Look how the cat is climbing up the tree!
'Hinauf' (up) is very often combined as a separable prefix with verbs of movement, e.g. 'hinaufgehen' (to go up), 'hinauffahren' (to ride/drive up), or 'hinaufsteigen' (to climb up). In a main clause, 'hinauf' comes at the end.
Wir fahren mit dem Aufzug in den zehnten Stock hinauf.
We're taking the elevator up to the tenth floor.
To name the path or destination of the upward movement, a noun in the accusative is often placed before 'hinauf' (up). Typical examples are 'die Treppe hinauf' (up the stairs) or 'den Berg hinauf' (up the mountain).
Er lief die Treppe schnell hinauf, weil er spät dran war.
He ran quickly up the stairs because he was late.
high
'hoch' and 'hinauf' both have to do with being up or at a higher place. But 'hoch' describes a state or quality: something is tall, high, or located far up. 'hinauf' describes upward movement, usually away from a lower place toward a higher place. Learners can easily confuse the words because both are connected with the direction upward. A simple guideline is: 'hoch' describes what something is like; 'hinauf' describes where someone or something is moving to.

Nach der Pause steigt die Mitarbeiterin die Treppe hinauf.
After the break, the employee goes up the stairs.
Der Turm neben dem Bahnhof ist sehr hoch.
The tower next to the train station is very tall.