As for the show itself, I'll keep it simple:
The writing is fantastic, the animation is fantastic, the stories are immersive and the lessons taught are nearly invaluable. Compared to anything on CN, Nick, or Disney, this is quality stuff.
As for the fandom, I'd like to rectify a few things Zamoonda said:
"These images come from the adult fans of this show, called the Bronies. The Bronies come from the imaeboard known as 4chan.org. There are two boards in specific that I will talk about -- the /B/, also known as the Random board, as well as /Co/, known as the Comics & Cartoons board. The term Brony comes from /B/rony and /Co/lts. A /b/rony is a person who is a fan of the show but is primarily on /b/ board, whereas a /co/lt is a fan of the show but is primarily on the /co/ board."
Bronies no longer only come from /b/ & /co/. That stopped happening in February '11, the term "/b/rony" also fell off then with the advent of Equestria Daily. A few like myself still hold the /b/rony title, but that's our own doing; "brony" is the name for fans now. And the term /co/lt has no relation to MLP. It's existed long before.
"The community that has settled in the website, ponychan.net, is amazing. Just outstanding." I'd like to correct this. Ponychan has been known on numerous occasions to ban users for defending other users from trolls. Ban frequent donators to the site (even those who had given more than $400 out of the kindness of their heart), ban gift givers for defending their generosity, and so fourth. Ponychan is certainly not representative of the brony fandom in any way. We do not support the message of "we're better because we're nicer" that ponychan displays on almost a weekly basis. As the rest of the fandom call them: We don't support being a "Canterlot" pony. If you watch the episode named Sweet & Elite, the ponies of Canterlot are shown as excessively stuck up. Ponychan is compared to Canterlot by the rest of us. I would also like to state Equestria Daily does not represent the fandom either for the same reason.
To make this relevant, you absolutely must supervise your children if they wish to explore outside of the show. As the fandom was born on the internet, at least half of its content is +18. And google images can't tell the difference. Like was mentioned in another comment, telling them to ask you what to look up is a very good suggestion. Like for instance, if they wanted a wallpaper of Twilight Sparkle for their desktop. I mention the insight into the fandom because while I was correcting some information, it should also be known that the main base of fans are from sites like /b/ & /co/ of 4chan, and fim.413chan - The fandom is inherently +18.
So parents: Forgetting about internet, the show is absolutely remarkable. I'll bet it'd be hard to not get into the show yourself, that's how amazing the new iteration of My Little Pony is. Doesn't matter if you're my neighbor's house cat, the intended audience, some 20+ year old dude, or the Ice Cream Man. You WILL love this show. The letters to Princess Celestia at the end always so wonderfully close out the lessons being taught throughout the episodes. I could make this comment much longer with reasons why both you and your children should watch it, but that would take a few weeks.
Remembering the internet real quick: Supervise everything. /b/ & /co/ are obvious reasons. Various sites pooling images into Google being another reason. And generally the younger audience may not be mature enough for some Youtube videos. Also be advised of ponychan. It isn't as nice as it seems, as I've stated.
I'll close this out by saying the show is absolutely amazing, and if I could show it in Times Square on every single monitor at once, I would. I should watch it. Your cat should watch it. You should watch it. And considering all it teaches, your kids -with the utmost priority- should watch it.
I'm just some 19 year old guy that's been on the internet for 10 years, who likes ponies. And after you see this show, you'll like ponies too.
Some random brony.
Edit: There ARE good things that come from the fandom however. Like shirts! I had this delivered two days ago and am quite reluctant to take it off. welovefine com/1619-rainbow-dash-nouveau.html - So Parents, you can rock out with your kids in some pony wear if it ever came down to it :) - The show inspires so much, let it inspire your children.