mountain
The German word 'Berg' is a common noun that refers to a mountain. It is used in the same context as the English word 'mountain'. For example, 'I climbed the Berg' means 'I climbed the mountain'. The word 'Berg' can also be used in compound words, such as 'Gebirge' which means 'mountain range'.
We hike up the mountain.
The German verb 'wandern' is used to talk about leisurely walking or hiking. 'Auf' means on or towards, and 'den Berg' refers to 'the mountain'. So this phrase is announcing a plan to hike up the mountain.
The mountain is high.
'Der Berg' is simply 'the mountain' in German. 'Ist' comes from the verb 'sein' which is to be, and 'hoch' is high or tall. The sentence is a descriptive statement about the height of the mountain.
I see a mountain.
In this sentence, 'Ich' means 'I', 'sehe' is 'see' and comes from the verb 'sehen'. 'Einen Berg' is 'a mountain', using the accusative case because it is the direct object of the verb.