
verleihen
to lend
To make something available to someone for a certain period of time, often for a fee.
Die Stadtbibliothek verleiht auch E-Books.
The city library also lends e-books.
to lend / award / give
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to lend
To make something available to someone for a certain period of time, often for a fee.
Die Stadtbibliothek verleiht auch E-Books.
The city library also lends e-books.

to award
To officially grant someone an award, title, or special honor.
Dem Regisseur wurde für sein Lebenswerk ein Ehrenpreis verliehen.
The director was awarded an honorary prize for his life's work.

to give
To give something a particular quality or atmosphere.
Die goldenen Akzente verleihen dem Raum eine edle Note.
The golden accents give the room an elegant touch.
'Verleihen' is the inseparable form of the verb 'leihen' (to lend/borrow). The prefix 'ver-' here emphasizes the action of giving something away or leaving it to someone else.
Kannst du mir bitte deinen Stift leihen?
Can you please lend me your pen?
The verb 'verleihen' almost always requires two objects: the person who receives something is in the dative, and the thing being lent, awarded, or given is in the accusative. The structure is: someone 'verleiht' [person in the dative] [thing in the accusative].
Die Universität verleiht dem Professor die Ehrendoktorwürde.
The university awards the professor an honorary doctorate.
The accusative object reveals the meaning: if it is an object (book, car), it means 'leihen' (to lend). If it is an honor (prize, title), it means 'zuerkennen' (to award). If it is a quality (shine, touch), it means 'geben' (to give).
Ich verleihe meine Werkzeuge nicht gerne.
I don't like lending my tools.
In the meaning 'zuerkennen' (to award), 'verleihen' is always combined with official honors. Typical phrases are: 'einen Preis verleihen' (to award a prize), 'einen Orden verleihen' (to award a medal), 'eine Auszeichnung verleihen' (to confer an award), or 'einen Titel verleihen' (to confer a title).
Der Nobelpreis wird jedes Jahr im Dezember verliehen.
The Nobel Prize is awarded every year in December.
In this meaning, the subject is often a thing or an abstract concept that gives a place or situation a particular quality. The structure is: [thing] 'verleiht' (gives) [something/someone] [a quality].
Die vielen Kerzen verliehen dem Raum eine festliche Atmosphäre.
The many candles gave the room a festive atmosphere.
to award / to distinguish
Auszeichnen and verleihen can both be used in an official ceremony in which someone receives a prize or medal. Auszeichnen emphasizes that someone is honored for a special achievement, while verleihen places more emphasis on the official act of granting the award. Choose between them depending on whether the focus is on the honor or on the presentation of the award.

Der Bürgermeister verlieh der jungen Musikerin die Ehrenmedaille.
The mayor awarded the young musician the Medal of Honor.
Die Jury zeichnete die junge Musikerin für ihre besondere Leistung aus.
The jury honored the young musician for her special achievement.