
anliegend
close-fitting
Fitting closely to the body; not wide or loose. Mostly used for clothing.
Sie trug ein eng anliegendes, schwarzes Kleid.
She wore a close-fitting black dress.
close-fitting / adjacent / attached
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close-fitting
Fitting closely to the body; not wide or loose. Mostly used for clothing.
Sie trug ein eng anliegendes, schwarzes Kleid.
She wore a close-fitting black dress.

adjacent
Directly neighboring; bordering on something.
Die anliegenden Grundstücke gehören ebenfalls der Gemeinde.
The adjacent plots of land also belong to the municipality.

attached
Attached as an enclosure to a letter or email.
Die anliegende PDF-Datei enthält die Rechnung für Ihre Bestellung.
The attached PDF file contains the invoice for your order.
'Anliegend' (close-fitting/adjacent/attached) is the present participle of the verb 'anliegen' (to lie against; to adjoin; to be enclosed). The meanings of the adjective can be derived from it: clothing that 'am Körper anliegt' (fits closely to the body), a plot of land that 'an ein anderes anliegt' (borders another one), or a document that 'einem Brief anliegt' (is enclosed with a letter).
Das T-Shirt liegt sehr eng an.
The T-shirt fits very tightly.
The meaning becomes clear from the noun. In connection with clothing, it means 'eng sitzend' (close-fitting). With plots of land or places, it means 'benachbart' (adjacent). In letters or emails, it means 'beigefügt' (attached/enclosed).
Sie kaufte ein eng anliegendes Top.
She bought a close-fitting top.
In the meaning 'beigefügt' (attached/enclosed), 'anliegend' (attached) is used mainly in formal written language, especially in business letters and emails. It sounds more formal and somewhat detached.
Die anliegende Rechnung bitten wir Sie, innerhalb von 14 Tagen zu begleichen.
We kindly ask you to pay the attached invoice within 14 days.
In formal correspondence, the phrasing 'Anliegend erhalten Sie ...' (Please find attached ...) or 'Anliegend übersenden wir Ihnen ...' (We are sending you attached ...) is often used. Here, 'anliegend' stands at the beginning of the sentence.
Anliegend erhalten Sie die gewünschten Unterlagen.
Please find attached the requested documents.
neighboring / adjacent
Benachbart and anliegend can both refer to something located directly next to something else. However, “anliegend” places greater emphasis on directly bordering or belonging to a particular area and therefore often sounds more factual. Use “benachbart” for general proximity and “anliegend” for areas that directly border something.

Die anliegende Fläche gehört zum Grundstück der Schule.
The adjacent area belongs to the school's property.
Das benachbarte Dorf ist von unserem Haus aus schnell zu erreichen.
The neighboring village can be reached quickly from our house.