na-adjective
Describes something that evokes a sentimental longing for the past, or has a deliberately retro style.
この喫茶店は懐古的な雰囲気が漂っている。
This coffee shop has a nostalgic atmosphere.
彼の服装はいつも懐古的で、昭和のスタイル
His clothing is always old-fashioned; he prefers Showa-era styles.
レトロ is a more casual, modern loanword for retro style, while 懐古的 has a slightly more literary or formal tone.
Compound of 懐古 (kaiko, 'reminiscence' or 'nostalgia') and the adjectival suffix 的 (-teki, '-like').