die Durchführung
implementation
The realization or execution of a plan, event, or measure.
Die Durchführung des Experiments dauerte mehrere Stunden.
The implementation of the experiment took several hours.

implementation / feedthrough
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implementation
The realization or execution of a plan, event, or measure.
Die Durchführung des Experiments dauerte mehrere Stunden.
The implementation of the experiment took several hours.

The word consists of 'durch' (through) and 'Führung' (guidance/leading). It describes the 'Hindurch-Führen' (leading through) of a process from beginning to end, or the guiding of something through an obstacle.
Die Durchführung der Reformen war komplizierter als gedacht.
The implementation of the reforms was more complicated than expected.
'Die Durchführung' (implementation/execution) is the noun corresponding to the separable verb 'durchführen' (to carry out). When you carry something out, the result is the 'Durchführung' (implementation).
Wir führen eine Umfrage durch. Die Durchführung dauert etwa eine Woche.
We are conducting a survey. The implementation takes about a week.
This word is often used in formal contexts. Typical combinations are 'die Durchführung eines Plans' (the implementation of a plan), 'einer Studie' (of a study), 'einer Veranstaltung' (of an event), or 'eines Experiments' (of an experiment).
Die Organisation war für die Durchführung des Festivals verantwortlich.
The organization was responsible for the implementation of the festival.
You can recognize the technical meaning from words like 'Kabel' (cable), 'Rohr' (pipe), 'Wand' (wall), or 'wasserdicht' (watertight). In all other cases, the general meaning 'Realisierung' (implementation/realization) is meant.
Der Elektriker bohrte ein Loch für die Kabel-Durchführung.
The electrician drilled a hole for the cable feedthrough.
organization
'die Organisation' and 'die Durchführung' often belong to the same situation, for example with an event or a project. 'Organisation' means the planning and structuring: dates, tasks, rooms, and people have to be prepared. 'Durchführung', on the other hand, means that the plan is actually carried out. The words can be confused because both are needed for something to succeed. Put simply: the organization happens mainly beforehand; the Durchführung happens when it is actually done.

Für die Durchführung des Kurses braucht das Team noch zwei Helfer.
The team still needs two helpers to run the course.
Mein Vater übernimmt die Organisation des Familienfestes, aber nicht das Kochen.
My father is taking care of organizing the family celebration, but not the cooking.