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.

'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.
bed
'das Bett' and 'das Körbchen' can both have to do with sleeping. 'das Bett' is the normal place for people to sleep. In this meaning, 'das Körbchen' is usually a small, soft sleeping place for a pet, especially a dog or cat. Learners may confuse the words because people can also say 'ins Körbchen gehen' (to go to bed) affectionately or jokingly. For people in normal everyday language, however, you say 'ins Bett gehen' (to go to bed). 'Körbchen' fits mainly with animals or in very playful language.

Der Hund liegt zufrieden in seinem Körbchen neben der Tür.
The dog is lying contentedly in his pet bed next to the door.
Nach der Arbeit lege ich mich kurz aufs Bett.
After work, I lie down on the bed for a bit.