This simple project demonstrates how yeast breaks down sugars by decomposing a banana. It involves putting two slices of banana into two plastic bags and putting yeast on one, and then observing how the banana slice covered in yeast decays more quickly than the plain slice. You could use this to demonstrate how yeast effects decomposition, or how yeast feeds.
Although this project requires petri dishes and some growth medium (a substance that contains what yeast consumes), it can still be very informative for children. You could use it to demonstrate whether or not yeast displays one of the essential characteristics of a living organism -- growth. This could make a very professional looking project, but unlike the others mentioned here, it would also require the most technical explanation since the growth medium would need to be explained.
Using yeast's reaction to sugary water to blow up a balloon is a great way to demonstrate how yeast metabolizes its food. This project demonstrates yeast's metabolic process by showing how it takes sugar (one of the things yeast consumes) and converts it to carbon dioxide gas (which fills the balloon). You could use this experiment to demonstrate that yeast is alive since it shows that yeast metabolizes food, which (along with growth) is a characteristic of living things.
Yeast is very helpful in processes such as baking and fermentation, but it is also a good stand-in for bacteria. Because of this similarity, you can use yeast to experiment with an alternative means of pasteurization (removing bacteria from liquids) that uses ultra violet (UV) light instead of heat. The most involved parts of this project are setting up a rig that will let you measure the carbon dioxide gas released from the liquid you are using (a measuring cylinder, rubber stopper and plastic tube are great for this), and finding a UV light. This is a practical experiment with real world use and can show how science experiments are used in the food industry.