bleiben
to stay
To remain in a place and not leave.
Wegen des Regens bleiben wir heute zu Hause.
Because of the rain, we're staying at home today.

to stay / remain
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to stay
To remain in a place and not leave.
Wegen des Regens bleiben wir heute zu Hause.
Because of the rain, we're staying at home today.

Although 'bleiben' (to stay/remain) does not describe movement, it always forms the perfect tense with the auxiliary verb 'sein' (to be). This is an important exception that must be learned by heart.
Ich bin gestern länger im Büro geblieben.
I stayed at the office longer yesterday.
To express that a state does not change, you combine 'bleiben' (to remain) directly with an adjective. The adjective is not declined.
Auch in der schwierigen Situation blieb er ganz entspannt.
Even in the difficult situation, he remained completely relaxed.
When you hold on to an opinion or decision, you use the fixed preposition 'bei' with the dative: 'bei etwas bleiben' (to stick with something).
Er bleibt bei seinem Plan, nächstes Jahr umzuziehen.
He is sticking with his plan to move next year.
Common expressions with 'bleiben' (to stay/remain) are 'in Kontakt bleiben' (to stay in touch), 'am Ball bleiben' (to keep at it / stay on the ball), and 'gesund bleiben' (to stay healthy, as a wish).
Lass uns auch nach deinem Umzug in Kontakt bleiben.
Let's stay in touch even after you move.
In the meaning 'übrig sein' (to be left over), 'bleiben' (to remain) often appears with quantities. The sentences often begin with 'Es ist/sind ...' (There is/are ...).
Nach der Party sind noch viele Getränke geblieben.
After the party, many drinks were still left over.
In a very formal or literary context, especially when it is about war, 'bleiben' (to remain) can mean 'sterben' (to die). This usage is very rare in everyday language.
Viele Soldaten sind auf dem Schlachtfeld geblieben.
Many soldiers fell on the battlefield.
to be
'sein' and 'bleiben' can both describe a place or a state. 'sein' simply says that someone or something is in a place or has a quality. 'bleiben' emphasizes that nothing changes: someone does not leave, or a state continues. So you can be in the office, but 'im Büro bleiben' (to stay in the office) means that you do not leave there. Learners confuse the words because both can be used with place expressions and adjectives. If you only mean the current state, 'sein' fits. If you mean duration or no change, 'bleiben' fits.

Wegen des Regens bleibe ich nach dem Unterricht noch in der Schule.
Because of the rain, I'm staying at school after class.
Heute ist ihr Chef im Büro.
Her boss is in the office today.