These are two big words often used in the geospatial world but who really knows or cares what they mean? Well now you can alllow yourself to be "In the Know".
Topology is the arrangement for how point, line, and polygon features share geometry. In other words, it's provides a means to make sure all of your pipes are connected to all of the network structures such as valves, hydrants, and/or manholes, etc. In addition you can make sure that there are no improper overlaps or intersections as in a tax parcel layer so your maps accurately represent what's out there in reality.
More info on Topology
Geometric Networking is just a fancy way of saying that all of your points, lines, and polygons have connectivity and can actually "talk" to each other. It creates a model of your network which can be very useful for managing water distribution systems, electrical lines, gas pipelines, telephone services, and streams within the same drainage basin.
More info on Geometric Networks
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Jon get's a little hair-brained in his latest tutorial videos when he dons a hard hat. Check them out at http://www.youtube.com/user/Cloudpointgeo