Heat flux is like breathing hot air into your hands. Imagine you are holding your hands in front of your mouth and you breathe out a warm gust of air. This warm air touching your hands is like heat flux.
Heat flux is the amount of heat that passes through a surface in a given time period. When something is hotter than something else, it wants to give its heat away. This is kind of like how you want to give your toys away when you're bored of them. The heat flows from the hot thing to the cooler thing, which is like you giving your toys to your little brother or sister.
The rate at which the heat flows is called heat flux. This is like how fast you might decide to give away your toys. If you give them away quickly, that's like a high heat flux. If you take your time, that's like a low heat flux.
Heat flux is important to understand because it affects how things work. For example, if you touch a hot stove, the heat flux from the stove to your hand is very high, and you can get burned. But if you touch the same stove with an oven mitt on your hand, the heat flux is much lower, and you don't get burned.
So, heat flux is just a fancy name for how fast heat moves through something. And just like you can control how quickly you give away your toys, we can control how quickly heat moves through different things.