Extranuclear inheritance is when something that is not in the cell's nucleus, where all the important genetic information is stored, gets passed down from parent to child. Imagine your cells are like a house, and the nucleus is like a really important room where your parents keep all the important stuff, like your birth certificate and family pictures. But there are other things in the house that can also be passed down from generation to generation, like a family heirloom that comes from grandma's side of the family.
Similarly, extranuclear inheritance involves things that are passed down from the cytoplasm, which is the gooey substance that fills the cell outside of the nucleus. This cytoplasm contains a lot of tiny structures called organelles, and two organelles in particular, mitochondria and chloroplasts, are important for extranuclear inheritance.
Mitochondria are like the power stations of the cell, and they convert food into energy that the cell can use. Chloroplasts are only found in plant cells, and they help produce food through a process called photosynthesis. These organelles have their own DNA that is separate from the DNA in the nucleus. When a cell divides, the cytoplasm also gets divided up, and this can result in uneven distribution of mitochondria and chloroplasts between the daughter cells. As a result, certain traits or diseases associated with these organelles can be inherited from the mother (since mitochondria and chloroplasts are usually inherited solely from the egg) even if the nuclear DNA comes from both parents.
So in summary, extranuclear inheritance is like inheriting a family heirloom that isn't kept in the important room where all the other family documents are stored. Instead, it comes from other parts of the house that can sometimes have their own unique features and characteristics that get passed down from generation to generation.