die Luft
air
The mixture of gases that surrounds the Earth and that living beings need in order to breathe.
Lass uns nach draußen gehen, um frische Luft zu schnappen.
Let's go outside to get some fresh air.

air
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air
The mixture of gases that surrounds the Earth and that living beings need in order to breathe.
Lass uns nach draußen gehen, um frische Luft zu schnappen.
Let's go outside to get some fresh air.

'Luft' (air) is a very productive base word for many compound nouns. When you see 'Luft-' at the beginning of a word, it often has to do with air, flying, or the sky, e.g. in 'Luftballon' (balloon), 'Luftdruck' (air pressure), or 'Flugzeug' (airplane).
Der Wetterbericht meldet hohen Luftdruck.
The weather report is forecasting high air pressure.
In connection with breathing, 'Luft' (air) is often used with verbs like 'Luft holen' (to take a breath) or 'die Luft anhalten' (to hold one's breath). The expression 'an die frische Luft gehen' means to go outside.
Nach dem langen Meeting musste ich erst einmal tief Luft holen.
After the long meeting, I first had to take a deep breath.
In the meaning of 'space', 'Luft' (air) is often used to express a lack, e.g. 'kaum Luft haben' (to have hardly any space). The idiom 'Luft nach oben haben' means that there is still room for improvement.
Mit all den Koffern im Auto haben wir kaum noch Luft zum Sitzen.
With all those suitcases in the car, we hardly have any space left to sit.
The idiom 'etwas liegt in der Luft' (something is in the air) means that you can sense a certain mood or an upcoming event. The subject is the thing that is expected.
Vor der wichtigen Ankündigung lag eine spürbare Anspannung in der Luft.
Before the important announcement, a noticeable tension was in the air.
The expression 'aus der Luft gegriffen sein' (to be plucked out of thin air) describes a claim that has no real basis and is invented. It is often intensified with adverbs like 'völlig' (completely) or 'total' (totally).
Der Vorwurf, er habe das Geld gestohlen, war völlig aus der Luft gegriffen.
The accusation that he had stolen the money was completely made up.
The idiom 'jemanden an die frische Luft setzen' (to put someone out into the fresh air) is a colloquial way of saying that someone is being thrown out or dismissed. The person who is dismissed is in the accusative.
Weil er die Miete nicht zahlte, wurde der Mieter an die frische Luft gesetzt.
Because he didn't pay the rent, the tenant was thrown out.
place / space
'Platz' and 'Luft' can both mean free space, but they are used differently. 'Platz' is the normal word when something or someone fits somewhere or has enough room. In this meaning, 'Luft' refers more to free distance or room to move. For example, you say that you need more 'Luft zum Arbeiten' (room to work) or 'Luft zum Bewegen' (room to move). Learners confuse the words because 'Luft' here does not mean the gas you breathe. As a rule of thumb: 'Platz' is free space for things or people; 'Luft' is often extra distance or leeway.

Lass beim Einparken etwas Luft zur Mauer.
Leave a little space between the car and the wall when parking.
Im Restaurant war heute kein Platz mehr für sechs Personen.
There was no room left in the restaurant today for six people.