
der Atem
breath
The air that living beings breathe in and out.
An kalten Tagen kann man seinen eigenen Atem sehen.
On cold days, you can see your own breath.
breath
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breath
The air that living beings breathe in and out.
An kalten Tagen kann man seinen eigenen Atem sehen.
On cold days, you can see your own breath.

to be out of breath
To breathe quickly and heavily after physical exertion.
Nachdem er zum Bus gerannt war, war er völlig außer Atem.
After he had run to the bus, he was completely out of breath.

to have staying power
To show a lot of endurance and patience with a difficult or lengthy task.
Für dieses Marathon-Projekt braucht man wirklich einen langen Atem.
For this marathon project, you really need to have staying power.
'Der Atem' (breath) is the noun that belongs to the verb 'atmen' (to breathe). While 'atmen' describes the action, 'der Atem' is the air that you move while doing it.
Er atmet sehr ruhig, wenn er schläft.
He breathes very calmly when he sleeps.
Common verbs used with 'Atem' (breath) are 'tief Atem holen' (to take a deep breath) and 'den Atem anhalten' (to hold one's breath).
Vor dem Sprung ins kalte Wasser hielt er den Atem an.
Before jumping into the cold water, he held his breath.
The expression 'außer Atem sein' (to be out of breath) is a fixed unit. It describes the state after great physical exertion, when you have to breathe quickly.
Ich bin die Treppe hochgelaufen und bin jetzt total außer Atem.
I ran up the stairs and am now totally out of breath.
The expression 'einen langen Atem haben' (to have staying power) is figurative. It means that someone has a lot of patience and endurance for a lengthy task.
Um eine neue Sprache zu lernen, muss man einen langen Atem haben.
To learn a new language, you need to have staying power.
air
Luft and Atem both occur in the context of breathing. Someone who can barely get any Luft feels that there is not enough air to breathe. Someone who is außer Atem is breathing quickly and heavily after exertion.

Nach dem schnellen Lauf war Lea völlig außer Atem.
After the fast run, Lea was completely out of breath.
Nach dem schnellen Lauf bekam Lea kaum noch Luft.
After the fast run, Lea could barely get enough air.