The long story short is that on the microscopic level mould — which, as you might already know, is a fungus — grows in tiny strands called Hyphae. Those hyphae aren’t visible to the naked eye, so even though you can see a big section of your bread or cheese or fruit or vegetables that have mould on it and cut it off, there are probably additional strands of the mould colony spidering through the soft parts of whatever food it is that’s gone off.
This is less of an issue with foods that are dense and hard, such as hard cheese and cured meats. For soft and porous foods though, including bread or veggies, this means cutting off the “bad part” may not eliminate the problem. Of course, your safest bet is to just throw the spoiled food away. Whatever you choose to do, this video from the folks at DNews will help you make the best call for your health and your kitchen.