die Einheit
unity
The state of cohesion and agreement; the solidarity of a group or country.
Die Mannschaft demonstrierte große Einheit auf dem Spielfeld.
The team demonstrated great unity on the field.

unity / unit
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unity
The state of cohesion and agreement; the solidarity of a group or country.
Die Mannschaft demonstrierte große Einheit auf dem Spielfeld.
The team demonstrated great unity on the field.

The word 'Einheit' (unity/unit) is derived from the number 'ein' (one). The ending '-heit' forms an abstract noun that describes the state of 'being one' or of cohesion.
Die Einheit des Teams war der Schlüssel zum Erfolg.
The unity of the team was the key to success.
The context reveals the meaning: In the political or social sphere, it is about cohesion. In connection with numbers and measurements, such as 'Maßeinheit' (unit of measurement), it means a measuring unit. In a military or organizational context, it is a group, and in textbooks or buildings, a self-contained part.
Die politische Einheit des Landes ist in Gefahr.
The political unity of the country is in danger.
The phrase 'die Deutsche Einheit' (German Unity) is a fixed historical term and refers to the reunification of Germany in 1990. In this context, the word is always capitalized.
Am 3. Oktober wird der Tag der Deutschen Einheit gefeiert.
German Unity Day is celebrated on October 3.
In the meaning 'abgeschlossener Teil' (self-contained part), 'Einheit' (unit) is often used as the base word in compounds. Common examples are 'Lerneinheit' (learning unit), 'Unterrichtseinheit' (teaching unit/lesson unit), or 'Wohneinheit' (residential unit).
Unsere Wohnung ist die größte Wohneinheit in diesem Haus.
Our apartment is the largest residential unit in this building.
piece
'das Stück' and 'die Einheit' can both mean something individual within a larger quantity. 'Stück' is used very often in everyday life when counting things or referring to a single part, for example 'ein Stück Kuchen' (a piece of cake) or 'drei Stück Seife' (three bars/pieces of soap). 'Einheit' sounds more precise and often somewhat more factual. It can be a fixed unit of measurement, such as liters or kilograms, or a self-contained part, for example 'eine Lerneinheit' (a learning unit). Learners may confuse the words because both refer to something clearly separate or bounded. For ordinary goods and parts, 'Stück' is usually more natural; for measuring, learning, or organization, 'Einheit' fits better.

Morgen wiederholt Herr Demir die letzte Einheit, weil viele Fragen offen sind.
Tomorrow, Mr. Demir will review the last unit because many questions are still unanswered.
Zum Kaffee nehme ich nur ein kleines Stück Kuchen.
With my coffee, I'll just have a small piece of cake.