
das Körbchen
small basket
A small basket, often used for collecting berries or mushrooms, or for carrying smaller items.
Die Kinder sammelten Erdbeeren in ihren kleinen Körbchen.
The children collected strawberries in their little baskets.
basket / pet bed
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small basket
A small basket, often used for collecting berries or mushrooms, or for carrying smaller items.
Die Kinder sammelten Erdbeeren in ihren kleinen Körbchen.
The children collected strawberries in their little baskets.

pet bed
A soft, padded sleeping place for a pet, especially for a dog or cat.
Der Hund liegt zufrieden in seinem Körbchen und schläft.
The dog is lying contentedly in his pet bed and sleeping.

to go to bed
An informal and often affectionate way of telling someone to go to bed.
Es ist schon spät, Zeit für dich, ins Körbchen zu gehen.
It's already late; time for you to go to bed.
'Körbchen' (small basket) is the diminutive form of 'der Korb' (the basket). The ending '-chen' signals that something is small and makes the noun neuter ('das Körbchen').
Er pflückte ein paar Pilze und legte sie in sein Körbchen.
He picked a few mushrooms and put them in his little basket.
The meaning depends on the context. If it is about a pet, the sleeping place is meant. If it is an informal request directed at a person, it means 'bed'. In other cases, it usually means a small basket.
Der Hund rollte sich in seinem Körbchen zusammen.
The dog curled up in his pet bed.
In the meaning 'sleeping place for pets', it is often used as a command. A typical sentence is the command to a dog: 'Geh in dein Körbchen!' (Go to your bed!) or 'Platz im Körbchen!' (Into your bed!).
Immer wenn es an der Tür klingelt, schicke ich den Hund in sein Körbchen.
Whenever the doorbell rings, I send the dog to his bed.
The expression 'ins Körbchen gehen' (to go to bed) is an informal and often affectionate or humorous way of saying that someone is going to bed. It is used only in colloquial speech.
Für mich ist es Zeit fürs Körbchen, ich muss morgen früh raus.
It's bedtime for me; I have to get up early tomorrow.
cup
The claimed confusion involving a bra is not supported by the accepted meaning of Körbchen. Cup refers here to the cup itself or its letter size; in the meanings given, Körbchen means only a small basket, a sleeping place for a pet, or an invitation to go to bed.

Der Hund schläft in seinem Körbchen.
The dog sleeps in its basket.
Sie trägt einen Büstenhalter mit Cup B.
She is wearing a bra with a B cup.