First of all, the answers by @Eric and Peter Schneider are already good. Instead of always explaining stuff by words, let the kids try to find it out as much as possible by themselves, if possible. Guide them, encourage them to try this and this, and if they claim an idea about it, let them prove it. That's just how real science works, too (without the guidance, of course).
And if the kids want to know more, explain it on a level they understand - though underlying mechanisms are often hard to understand, even by adults.
Sometimes, there are intermediate explanations as the example of the slippery ice from Feynman's video, which can be explained by a thin film of water, melted from the ice under pressure. But the next step, why water behaves like that, while other substances do not, is already more complicated.
Sometimes, there is also no good intermediate step. One of the most head questions is "Why is the sky blue?", where most adults don't have an answer for. As physicist, I know it's about Raman and Rayleigh scattering of sunlight in the atmosphere, but I really have no idea how to explain this to an adult, or even a child. I can just say that sunlight is scattered, and that this happens more to blue than other colors... which is not very satisfying.
Back to magnets, I would explain it as follows:
The kid should already have found out, that a magnet has a north and a south pole , and that poles can repel or attract each other, and that this already works from some distance.
Now, a magnet consists of many many, very tiny mini-magnets, which are all aligned into the same direction, and can not move / rotate.
One prove for this is to break a magnet into two pieces, which each on it's own are perfect magnets with north and south pole.
Iron also contains this mini-magnets, but they are not aligned and have random orientations. When a magnet is placed near to iron, the mini-magnets start to rotate and align into the direction of the magnet. This is because the poles of the magnet attract the counter-poles of the mini-magnets.
The iron becomes magnetic, and attracts the magnet (and vice-versa). If the magnet is removed, each of the mini-magnets start to move to a random orientation again, and the iron looses its magnetic property.
Inside steel, the mini-magnets can't rotate that easily, they only do it when there is a magnet near to them. As consequence, they remain in their orientation, even when the magnet is removed. The steel becomes a (weak) magnet itself.
Other materials may not contain any mini-magnets, or those mini-magnets are not aligned and absolutely unable to rotate.
However, this does not explain what this mini magnets are or why they / magnetic fields exist. (And there's also no fundamental answer why magnetism itself exists.)
By the way: Did you ever notice that earths north pole actually is a magnetic south pole? A compass needle is a magnet, and its north pole is marked with an
N. So, this side is attracted by a magnetic south pole, which must be at the geographic north pole.
And a last comment:
I don't know if you know who Richard Feynman from the video is. He is one of the greatest physicists of the 20th century and got the nobel prize for his work on quantum electro dynamics. This is very complicated stuff, and he managed to teach about it in the most clearest way possible. His Feynman diagramms are the standard to describe processes in particle and quantum physics. So, if you need someone explaining complicated stuff "for dummys", he's your man.