What is a free-standing tent? What are the advantages of a free-standing tent as opposed to a tent that isn't, and what are the disadvantages?
A free standing tent can be put up in a location that won't let you put pegs into the ground, such as on a rocky surface, because it establishes structure of its own and the pegs are just to keep it from blowing away. You can tie the tent to rocks or trees if pegs won't go into the ground. In a pinch, you can use rocks inside the tent to keep it down, or rely on your own weight.
There are other benefits too. In 30 years of camping I've set up on solid rock maybe twice. But I can't count the number of times I've unpegged the wet tent, carried it somewhere sunnier than where I pitched it, and even rolled it on one side to expose the wet base to a breeze. I've also unpegged a tent that still had bedding in it, put it in a canoe, and moved it to another (very nearby) site and then pegged it back out again.
If you plan to camp with small children, then you should enjoy being able to set up the tent in the least tent-peg-friendly location of all (and one where both rocks and trees are in remarkably short supply): your living room. Great place to practice setup and for the kids to practice sleeping in it.
As others have said, the main advantage of a free standing tent is that it doesn't require stakes or rope tied to external fixed objects to stand up. Of course there are downsides too. This generally means there will be more poles and the tent will therefore be heavier for the same internal size. Personally, I think the advantages only make sense in limited conditions. A free standing tent is great if the only surfaces you have to place the tent on don't allow for stakes and the conditions aren't too windy. That can occur, but in my experience this combination is pretty uncommon.
I have a small tent that requires a minimum of 3 stakes to stand. Two more stakes are optional and only necessary to keep the tent anchored in case of high wind. Camping in a forest is not a problem. The forest floor is always spongy enough that installing a stake is simply a matter of pushing it in. It takes about a second and you're done.
The most common difficulty I run into with this system is when camping in the desert. The ground tends to be dry hard-packed dirt. It can take a couple of minutes per stake to get them the 6-8 inches into the soil. This usually takes a bunch of twisting and pushing. I can't bang my tent stakes since they are aluminum with a hook loop on top. Banging only deforms the loop.
Most of the time I get the stakes in. The worst is when two stakes are already in and I just can't get the third in far enough. That means I have to move at least one of the other stakes to allow re-positioning the last one and trying at a different location. That happens to me about once of the 10 nights or so I spend in Arizona in that tent a year. So far I've always gotten the stakes in at the chosen campsite after a retry or two at most. Sometimes you can pour a little water over where you want to put the stake to soften the soil, but that doesn't really work as well as it sounds. So anyway, a self-standing tent would have helped, but the tent I have didn't keep me from camping in any of those places. In the end, I'd still rather futz with the stakes a little more some of the time than have a larger and heavier tent.
Only one time in the nearly 30 years I have been using my little tent did the ground conditions foil it completely, and that was in the White Mountains of New Hampshire. I was on top of Bondcliff when it was time to find a place to set up camp. I knew Bondcliff was broad enough on top and just assumed I could find a place to put the tent. I was wrong. Either there was bare rock or thinly covered rock, or too much of a slope, or thick knee-high alpine bushes. A free standing tent would have worked, although keeping it from getting blown off the mountain would have been a issue. I probably could have dealt with that by using enough rocks for weights in the right places, especially if the tent wasn't too tall. In the end I ended up with my sleeping bag under the stars. I piled some rocks around as a windbreak. That helped, but it was still very windy that night and there was also a thunderstorm. Yes, I and my sleeping bag got pretty wet and it wasn't a pleasant night. Oh well, you gotta have a few adventures in life to look back on and tell stories about too.