die Befestigung
attachment
The process of fixing or fastening something in place.
Die Befestigung des Regals an der Wand dauerte eine Stunde.
Attaching the shelf to the wall took an hour.

attachment / fortification / fastener
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attachment
The process of fixing or fastening something in place.
Die Befestigung des Regals an der Wand dauerte eine Stunde.
Attaching the shelf to the wall took an hour.

'Die Befestigung' (attachment / fortification / fastener) is the noun related to the verb 'befestigen' (to fasten). Depending on the context, it can refer to the process of fastening, the result (a fortress), or the tool used for it (a screw).
Wir müssen das Zelt gut befestigen, damit es der Wind nicht wegweht.
We have to secure the tent well so the wind doesn't blow it away.
The meaning becomes clear from the context. If people are talking about a 'Schraube' (screw) or a 'Dübel' (wall plug/anchor), an object is meant. If it is about a 'Burg' (castle) or 'Mauer' (wall), a defensive structure is meant. If an action is being described, such as '... des Spiegels' (... of the mirror), the process is meant.
Für diese schwere Lampe brauchen wir eine spezielle Befestigung.
For this heavy lamp, we need a special fastener.
When the process of fastening is being described, the preposition 'an' with the dative often follows to indicate the location. The structure is: die Befestigung von etwas an etwas (the attachment of something to something).
Die Befestigung der Kamera an der Decke war kompliziert.
Attaching the camera to the ceiling was complicated.
When an object is meant, the word is often combined with verbs like 'kaufen' (to buy), 'suchen' (to look for), 'finden' (to find), or 'brauchen' (to need). In that case, people are talking about screws, wall plugs/anchors, hooks, or clamps.
Im Baumarkt habe ich die passenden Befestigungen für das Bild gefunden.
At the hardware store, I found the right fasteners for the picture.
fuse / backup / safety
'die Sicherung' and 'die Befestigung' can both have to do with fastening something. 'Befestigung' emphasizes that something is held firmly in one place, for example with screws, clamps, or a strap. 'Sicherung' emphasizes protection: something should not fall down, come loose, or become dangerous. The words can be confused because you often fasten something in order to secure it. The difference is the purpose: 'Befestigung' is more about 'How does it hold?', while 'Sicherung' is more about 'How is danger prevented?'

Wegen des starken Windes haben wir die Befestigung des Zeltes noch einmal geprüft.
Because of the strong wind, we checked the tent's fastenings again.
Beim Klettern kontrolliert Frau Wagner zuerst die Sicherung.
When climbing, Ms. Wagner checks the safety equipment first.