die Vorführung
screening / performance
The public presentation of a film, play, or artistic performance.
Die nächste Vorführung des Films beginnt um 20:15 Uhr.
The next screening of the film starts at 8:15 p.m.

screening / demonstration
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screening / performance
The public presentation of a film, play, or artistic performance.
Die nächste Vorführung des Films beginnt um 20:15 Uhr.
The next screening of the film starts at 8:15 p.m.

The word is derived from the verb 'vorführen' (to demonstrate, to show). It consists of 'vor' (in the sense of 'in front of others') and 'führen' (to lead). A 'Vorführung' is therefore an action in which something is shown or presented in front of an audience.
Der Zauberer bereitete seine nächste Vorführung vor.
The magician prepared his next performance.
The context makes clear which meaning is intended. If it is about cinema or theater, it means a screening or performance. If it is about a product, it means a demonstration. In an argument or interrogation, it can mean humiliation or exposure.
Die Vorführung des neuen Staubsaugers hat mich überzeugt.
The demonstration of the new vacuum cleaner convinced me.
In the context of art and culture, people often speak of a 'Filmvorführung' (film screening) or 'Theatervorführung' (theater performance). Common verbs are 'eine Vorführung besuchen' (to attend a screening/performance) or 'zur Vorführung gehen' (to go to the screening/performance).
Wir gehen heute Abend in die Spätvorführung des neuen Actionfilms.
Tonight we're going to the late screening of the new action film.
The meaning 'Bloßstellung' (humiliation/exposure) has a strongly negative connotation. It describes a situation in which someone is deliberately put into an embarrassing or humiliating position.
Das Interview entwickelte sich zu einer peinlichen Vorführung für den Politiker.
The interview turned into an embarrassing humiliation for the politician.
exhibition / issuing
'die Ausstellung' and 'die Vorführung' both mean that something is shown to an audience. 'Die Ausstellung' fits better for things you look at calmly, for example pictures, photos, or products. It often lasts several days or weeks. 'Die Vorführung' is more of an event: a film is shown, a play is performed, or someone demonstrates how a device works. The words can be confused because both can be public. As a simple guide: for objects to look at, you say 'Ausstellung'; for an action, a film, or a demonstration, 'Vorführung' is more likely.

Zur Vorführung der neuen Kaffeemaschine erklärt der Verkäufer jeden Schritt.
During the demonstration of the new coffee machine, the salesperson explains every step.
Im Rathaus sieht meine Schwester eine Ausstellung über modernes Wohnen.
At the town hall, my sister sees an exhibition about modern living.