
der Sessel
armchair
A comfortable, upholstered seat for one person that typically has armrests.
Er saß gemütlich im Sessel und las ein Buch.
He sat comfortably in the armchair and read a book.
armchair / chair
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armchair
A comfortable, upholstered seat for one person that typically has armrests.
Er saß gemütlich im Sessel und las ein Buch.
He sat comfortably in the armchair and read a book.

chair
In Austria and parts of southern Germany, the term for a simple chair, often without upholstery or armrests.
Stell bitte noch einen Sessel an den Küchentisch.
Please put another chair at the kitchen table.
Pay attention to the prepositions and the case. When you are moving toward the piece of furniture, it is 'in den Sessel' (into the armchair/chair, accusative). When you are already there, it is 'im Sessel' (in the armchair/chair, dative).
Setz dich doch in den bequemen Sessel am Fenster!
Go ahead and sit down in the comfortable armchair by the window!
In the standard meaning 'upholstered furniture', 'Sessel' (armchair) is often combined with adjectives that describe comfort or material. Typical phrases are 'bequemer Sessel' (comfortable armchair), 'gemütlicher Sessel' (cozy armchair), or 'Ledersessel' (leather armchair).
Für meine Leseecke wünsche ich mir einen gemütlichen Sessel mit hoher Lehne.
For my reading corner, I would like a cozy armchair with a high back.
Be careful: the meaning of 'Sessel' (armchair/chair) differs by region. In Austria and parts of southern Germany, the word often refers to a simple chair, for example at the dining table.
In Wien fragt man im Restaurant vielleicht: „Ist dieser Sessel hier noch frei?“
In Vienna, someone might ask in a restaurant: 'Is this chair here still free?'
chair / stool
Der Stuhl and der Sessel both refer to a piece of seating for one person. In standard German, a Sessel is usually softly upholstered and has armrests, while a Stuhl is more ordinary and often unupholstered. In Austria, however, Sessel can also mean a simple chair.

Im österreichischen Möbelgeschäft setzte ich mich auf einen einfachen Holzsessel.
In the Austrian furniture store, I sat down on a simple wooden chair.
Im deutschen Möbelgeschäft setzte ich mich auf einen einfachen Holzstuhl.
In the German furniture store, I sat down on a simple wooden chair.