High praise; great admiration. Often used as a noun or in the verb form '絶賛する' to indicate strong approval or acclaim.
その映画は批評家から絶賛を受けた。
That film received rave reviews from critics.
彼の演技は観客に絶賛された。
His acting was highly praised by the audience.
新商品の品質は業界で絶賛されている。
The quality of the new product is being widely praised in the industry.
Used adverbially to indicate that something is receiving high acclaim (e.g. in phrases like '絶賛上映中' = 'now playing to rave reviews').
新作が絶賛上映中だ。
The new release is now playing to rave reviews.
そのレストランは絶賛の的になっている。
That restaurant is being hailed (receiving high praise).
Colloquial/jocular use meaning 'currently' or 'in the middle of' — typically appears in the pattern '絶賛～中' (e.g., 絶賛多忙中) to jokingly emphasize a state.
只今、絶賛多忙中につき返信が遅れます。
I'm currently extremely busy, so my reply will be delayed. (humorous/colloquial)
彼は絶賛恋愛中らしい。
Apparently he's head-over-heels in love right now. (playful)