sich eignen für/zu
to be suitable for
To be suitable or appropriate for a particular purpose, task, or person.
Dieses Material eignet sich hervorragend für den Außenbereich.
This material is excellently suited for outdoor use.

to be suitable
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to be suitable for
To be suitable or appropriate for a particular purpose, task, or person.
Dieses Material eignet sich hervorragend für den Außenbereich.
This material is excellently suited for outdoor use.

'Eignen' is almost always used reflexively: 'sich eignen' (to be suitable). The reflexive pronoun must be adjusted to match the subject.
Ich eigne mich nicht für diese Aufgabe.
I am not suitable for this task.
The verb is used with the prepositions 'für' (for, plus accusative) or 'zu' (for/to, plus dative). 'Für' usually comes before a noun, while 'zu' often comes before a nominalized infinitive.
Diese Schuhe eignen sich gut für lange Wanderungen.
These shoes are well suited for long hikes.
The past participle 'geeignet' (suitable) is very often used as an adjective, often in the construction 'geeignet sein für' (to be suitable for). It has the same meaning as 'sich eignen für' (to be suitable for).
Er ist für die Position des Teamleiters gut geeignet.
He is well suited for the position of team leader.
to fit / suit / pass
'passen' and 'sich eignen' both say that something is good for a purpose or situation. 'passen' is very general and sounds more natural in everyday language, for example with appointments, colors, or plans. 'sich eignen' puts more emphasis on the purpose or task: something can be used well for it. Learners may confuse the words because both have to do with 'being suitable'. As a simple guide: an appointment suits you, while a tool or method is suitable for something.

Für diese Reparatur eignet sich ein kleiner Schraubenzieher.
A small screwdriver is suitable for this repair.
Am Montag passt mir ein Treffen im Restaurant besser.
On Monday, meeting at the restaurant suits me better.