つつ is a particle in Japanese that appears after the ます-stem form of verbs. When used, it indicates that (B) is an action that is happening at the same time as (A). This usually translates simply as ‘while (A), (B)’.
つつ is a formal grammar structure and will appear in writing more than in speech.
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環境（かんきょう）に悪（わる）いと知（し）りつつ、レジ袋（ぶくろ）を使（つか）い続（つづ）けている。
While I know that it is bad for the environment, I continue to use plastic bags.
インターネットでレシピを見（み）つつ、料理（りょうり）をしたので今日（きょう）の晩御飯（ばんごはん）は美味（おい）しいはずです。
Dinner tonight should be delicious since I cooked while looking at a recipe on the internet.
Caution - Unlike
ながら,
つつ is used more often when the (A) action is an ongoing state, rather than an actual physical action that involves movement.
ながら may be used for both physical motions and states.
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走（はし）りながら携帯（けいたい）でゲームをしていたら、電柱（でんちゅう）にぶつかった。
I bumped into a telephone pole because I was gaming on my phone while I was walking. (Natural Japanese)
走（はし）りつつ携帯（けいたい）でゲームをしていたら、電柱（でんちゅう）にぶつかった。
I bumped into a telephone pole because I was gaming on my phone while I was walking. (Physical action, unnatural Japanese)
仕事（しごと）に関係（かんけい）ないことを考（かんが）えながら仕事（しごと）をしていたら、大（おお）きなミスをしてしまった。
I made a big mistake at work because I was working while thinking about something unrelated to work. (Natural Japanese)
仕事（しごと）に関係（かんけい）ないことを考（かんが）えつつ仕事（しごと）をしていたら、大（おお）きなミスをしてしまった。
I made a big mistake at work because I was working while thinking about something unrelated to work. (Non-physical, natural Japanese)
Despite this, the (B) action in
つつ sentences may either be physical movements or ongoing states.