das Kleid
dress
A one-piece item of clothing for women and girls that covers the upper body and falls from the waist downward like a skirt.
Für die Hochzeit hat sie sich ein neues Kleid gekauft.
She bought a new dress for the wedding.

dress
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dress
A one-piece item of clothing for women and girls that covers the upper body and falls from the waist downward like a skirt.
Für die Hochzeit hat sie sich ein neues Kleid gekauft.
She bought a new dress for the wedding.

The word 'Kleid' (dress) belongs to the word family around 'Kleidung' (clothing). The related verb is 'sich kleiden' (to dress oneself). This connection helps you understand the basic meaning.
Sie kleidet sich immer sehr elegant.
She always dresses very elegantly.
There are special dresses for different occasions, which is reflected in many compound words. Common examples are 'Abendkleid' (evening dress), 'Sommerkleid' (summer dress), or 'Hochzeitskleid' (wedding dress).
Für den Sommerurlaub packe ich mehrere leichte Sommerkleider ein.
For the summer vacation, I’m packing several light summer dresses.
The figurative meaning of 'Kleid' (garment/covering) is used almost only in poetic or very descriptive language, often in connection with nature. Usually the preposition 'in' or the phrase 'ein Kleid aus ...' (a garment of ...) is used.
Im Winter trägt die Landschaft ein Kleid aus Schnee.
In winter, the landscape wears a garment of snow.
form / shape
'die Form' and 'das Kleid' can both have to do with the outer shape or appearance of something. 'Form' is the normal word when talking about the shape, structure, or way something is presented. 'Kleid' actually means a piece of clothing, but in elevated or figurative language it can mean the outer covering or appearance of something. This does not sound natural in every everyday sentence. If you are speaking clearly and neutrally about appearance or design, use 'Form'. 'Kleid' is more suitable in poetic or figurative language, for example with art, language, or ideas.

Die alte Geschichte erscheint in diesem Film in einem modernen Kleid.
The old story appears in this film in a modern guise.
Die Form der neuen Lampe passt gut zu dem runden Tisch.
The shape of the new lamp goes well with the round table.