der Himmel
sky
The space above the earth where clouds, the sun, the moon, and the stars are visible.
Nach dem Regen war der Himmel wieder strahlend blau.
After the rain, the sky was bright blue again.

sky / heaven
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sky
The space above the earth where clouds, the sun, the moon, and the stars are visible.
Nach dem Regen war der Himmel wieder strahlend blau.
After the rain, the sky was bright blue again.

The meaning of 'Himmel' depends strongly on the context. If it is about weather, astronomy, or flying, it means the sky above us. In a religious or spiritual context, it means the afterlife.
Die Wolken am Himmel sehen aus wie Tiere.
The clouds in the sky look like animals.
To describe a position, you use 'am Himmel' (in the sky). To express upward movement, you say 'in den Himmel' (into the sky).
Der Mond steht schon hell am Himmel.
The moon is already shining brightly in the sky.
The expression 'unter freiem Himmel' means 'outside' or 'in the open air'. It is often used for events such as concerts or overnight stays.
Das Konzert findet unter freiem Himmel statt.
The concert is taking place in the open air.
The expression 'der Himmel auf Erden' (heaven on earth) describes a state or place of perfect happiness. It is used to express an intensely positive feeling.
Dieser Urlaub am Meer war für mich der Himmel auf Erden.
That vacation by the sea was heaven on earth for me.
Earth / soil
'die Erde' and 'der Himmel' often form a contrast between below and above. 'die Erde' is the planet we live on, or, in fixed expressions, life here in this world. 'der Himmel' is the space above us with clouds, the sun, and stars. In religious contexts, 'Himmel' can also mean a place after death; then 'auf Erden' (on Earth) stands for life in this world. In everyday language, 'Erde' usually means our planet or the ground, while 'Himmel' usually means the visible space above us.

Wegen des Gewitters wird der Himmel am Nachmittag ganz dunkel.
Because of the thunderstorm, the sky will turn very dark in the afternoon.
Nach dem langen Flug war Jana froh, wieder auf der Erde zu stehen.
After the long flight, Jana was glad to be standing on the ground again.