Lolita is by far my absolute favorite fashion There are many different types of Lolita fashion that's popular in Japan - It's also sometimes referred to as Gothic Lolita - but there's also Elegant Lolita, Babydoll Lolita, Princess (Hime) Lolita, etc.
It takes victorian inspired fashion such as dresses and robes and big hair/hats/etc. It became popular in the 80s/90s with many "boy bands" in Japan who would cross dress in the elaborate dresses and high heels. (FUN FACT: Back in victorian ages, high heels were actually worn by men to make them look taller). The fans who enjoyed going to see these bands perform live began to wear similar costumes - We see this even in America too, how for example, Lady Gaga's fans dress in crazy costumes to emulate and show support for their favorite performers. Around the same time that all of this was going on, there were many popular Japanese fashion magazines which featured "Street Snaps" of people wearing this fashion (presumably on their way too or from a concert). Girls (and guys) buying these magazines, fell in love with the fashion and it took off as "everyday" wear not just something by fans of the bands. Later in the 90s, many anime featured lolita fashion as well which further helped spread the popularity of this trend. It's still incredibly popular to this day. Many girls now also see it as a way to "dress like a princess" and bring out their femininity.
I have worn lolita a few times myself, to concerts or parties or different occasions. It can be hard to find plus sized lolita fashion since Japanese girls are so small - Most of the time, a "large" or even "extra large" over there is like a US size 8 or 10.
The fashion trend has also spread to the west and some users (such as ETSY shops etc) carry more diverse items. There's also a US store now for Baby the Stars Shine Bright and a few other "Bigname" Lolita brands.
My favorite dresses are the ones with super cute prints, like animals or sweets and candy. Or ones with lots of ruffles and ribbons!
Here are some cool pics of girls wearing lolita fashion below: