This is the 3734th most frequent Japanese word.
さく
"さく" can mean "to bloom" or "a plan; a scheme," depending on context.
In this sentence, "さく" (saku) is used as a verb meaning "to bloom" to describe flowers opening, specifically cherry blossoms here.
公園で桜が咲いています。
Cherry blossoms are blooming in the park.
Here, "さく" (saku) is used colloquially and less commonly as a verb meaning "to creak" for doors or hinges producing a sound.
このドアは咲きますか?
Does this door creak?
In this context, "さく" (saku) metaphorically represents "to arise" or "to emerge," depicting the conception of new ideas.