These are paid subscritions to sites that send you a box of samples for you and/or your child every month.
I just heard of these recently when I saw a signup link for Bluum on a FB mom's group. I followed it and requested an invite; after a couple days I got an email saying I was "in" (like there was some kind of approval process or something) with a link to subscribe. For $11/month you get a box of "deluxe" product samples.
I wasn't sure this was worth the expense so I did some googling before signing up; turns out reviews are mixed. But I also learned there are other subscription boxes like Citrus Lane which is even more money but seems to be well-liked.
I do Citrus Lane, and I like it a lot. You do get some sample-sized stuff with Citrus Lane, but you also get toys/bigger stuff. I've really liked the boxes we've received. You can see what was in the boxes from the past few months on the website, and there are lots of bloggers who do monthly reviews. Check for discount codes if you decide to sign up - there are usually codes floating around.
I've done Bluum and Teethe Me. I got Bluum through a daily deal site, which was the only cost-effective way to do that one, because I don't think it was worth full price. Teethe Me was a lot better, but costs much more. I only did both for three months. I would like to try Citrus Lane, but will wait until a 20% deal appears or a daily deal site sells a 3-month membership.