I won't spend your time on a lengthy explanation, suffice it to say that it is the famed Japanese doll festival held in honor of girls and young ladies, with the wish that they will grow up healthy and beautiful and find a happy marriage. Rainbows and unicorns.
...and if stereotypical domestic bliss isn't your thing, the dolls are still a ton of fun.
切り絵 (pronounced key-ree-EH) is somewhat different from paper cutting or kirigami. For the paper-loving crowd, here's a quick breakdown of the terms:
papercutting or paper cutting: general English term for any art produced by cutting one or more sheets of paper; generally assumes a minimum of drawn media
切り紙, kirigami: Japanese term that translates as "cut paper"; a not-necessarily broad term for cut paper arts, usually referring to geometric shapes cut from folded paper (think "paper snowflakes" and you've pretty much got it).
紋きり, monkiri: a branch of kirigami that deals specifically with the folding and cutting of paper to produce familiar mon (or kamon) family crests and motifs
切り絵, kiri-e or kirie: as presented in this post, means "cut image"; a term for images cut from a single, unfolded sheet of paper, usually black, which can manifest either as linework or as a positive-negative reduction image
wycinanki: Polish papercuts, with the Lowicz-style being unique in the world of papercutting for the use of multiple layers of bright colors
Of course, kiri-e isn't the most common medium for hina dolls. Most traditional ones are hard dolls, clothed in silk and embellishments, with ceramic faces and hands:
Hina dolls are probably one of the most fascinating elements of Japanese craft culture for folks who enjoy softies and figure work. For more images and inspiration, may I recommend searching the terms おひな様 or ひな人形 on Google image search. There are some amazing sets out there.