zwar ... aber means "it's true ... but".
Ich habe zwar nicht gewonnen, (ich) bin aber sehr stolz auf diese Saison
It's true that I didn't win but I am very proud of this season
"zwar... aber" is a compound conjunction that connects two main clauses. The first clause contains "zwar" and the second "aber". This conjunction is for making adversative clauses in German ("Adversativsatz").
It is formed with normal structure: "zwar" Clause + "aber" Clause:
Es ist zwar nicht kalt hier, aber (es ist) recht grau
It's true that it's not cold here but it's really cloudy
Zwar ist es kalt hier, aber wir finden den Schnee so schön
It's true that it's really cold here but we think that the snow is so pretty
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