When I say "I'm Bored" it can mean any number of different things. Sometimes it means whatever I was doing previously is not longer managing to hold my interest and I really do just want some suggestions of things to do now. Or maybe I finished a project and I'm looking for a new one to start. Sometimes it means I've been sitting too long and I need to move around - or it means I'm physically tired and looking for something calm and still to do.
For me it is very often one of these two things: either I'm lonely or I need to get out of the house. My loneliness can be for different people. Maybe I'm missing my mom and need her attention for a while. Maybe I'm missing my friends and need to make some plans to see them. Or I could need to get up, get dressed and get out of the house, even for just a trip to the store. Sometime even the simple act of getting out of my PJs and brushing my teeth will be enough for me, and then I can happily go back to whatever I was doing before.
Your job is to find out what "I'm bored" means to you, your children, and your family.