I am not a professional cook, but I would understand them as follows: If the recipe says "chop the carrots", it means I have to cut them up, but it hasn't told me what shape or size the pieces should be. If it says "dice the carrots", it means cut them into small cubes. If it says "shred the carrots", then I need to use a grater to make them into pieces that are long and very thin. In England I don't think we would talk about shredded carrots, we would say grated carrots instead. Perhaps "shredded" would be used in America.

To chop is to cut up roughly, meaning in uneven sizes. You might chop fresh tomatoes to put them on a salad, and it doesn't really matter if they are big or small peices. To dice is to cut up more exactly, usually in squares. The recipe might say to dice to a certain size, like "carrots in a 1cm dice". You would dice an onion to add it to a salsa, for example, where you don't want to get a big piece. To shred is to cut so that the end result is long skinny pieces. You can shred cabbage for coleslaw for example. Food processors often have a "shredding disc" and allow you to process hard foods like potatoes or jicama into long and skinny pieces very easily. Here is an illustration of the difference between dicing and shredding: http://www.cookingenthusiast.com/how-to/tech2.shtml#dicing