abweisen
to reject
To reject or refuse a person, a request, an offer, or a suggestion.
Sie hat sein Angebot, ihr zu helfen, kühl abgewiesen.
She coolly rejected his offer to help her.

to reject / turn away
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to reject
To reject or refuse a person, a request, an offer, or a suggestion.
Sie hat sein Angebot, ihr zu helfen, kühl abgewiesen.
She coolly rejected his offer to help her.

'Abweisen' is a separable verb. The prefix 'ab-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Chef wies meinen Vorschlag sofort ab.
The boss rejected my suggestion immediately.
The verb is made up of the prefix 'ab-' (away) and the verb 'weisen' (to show, to guide). The literal meaning 'to point away' or 'to send away' is the basis for all meanings of the verb.
Der Hund wurde am Eingang des Supermarktes abgewiesen.
The dog was turned away at the entrance to the supermarket.
You can reject people ('einen Verehrer abweisen' — to reject an admirer) or their offers. Typical objects are: 'ein Angebot' (an offer), 'eine Bitte' (a request), 'ein Kompliment' (a compliment), or 'ein Vorschlag' (a suggestion).
Er hat ihr Jobangebot höflich, aber bestimmt abgewiesen.
He rejected her job offer politely but firmly.
In this meaning, 'abweisen' (to dismiss/reject) is used almost exclusively in a legal context. It is often used in the passive to report what happened to a lawsuit or motion.
Der Antrag wurde vom Gericht als unbegründet abgewiesen.
The motion was dismissed by the court as unfounded.
For materials, the adjective form 'abweisend' is very common. People speak of 'wasserabweisenden' Jacken (water-repellent jackets) or 'schmutzabweisenden' Oberflächen (dirt-repellent surfaces).
Diese Hose ist aus einem schmutzabweisenden Stoff gemacht.
These pants are made of a dirt-repellent fabric.
to accept / assume
'annehmen' and 'abweisen' are opposites when talking about an offer, request, suggestion, or application/motion. 'annehmen' means that you say yes or officially approve something. 'abweisen' means that you say no or reject something. In official or legal situations, an application or motion can be accepted/adopted or rejected/dismissed. Learners may confuse the words because both are often used with the same nouns, for example 'Antrag' (application / motion) or 'Vorschlag' (suggestion/proposal). Pay attention to the direction: 'annehmen' is approval, 'abweisen' is rejection.

Das Gericht weist den Antrag wegen fehlender Beweise ab.
The court dismisses the motion due to lack of evidence.
Der Verein nimmt den Vorschlag der Mitglieder an.
The association accepts the members' proposal.