Your local utility delivers the electricity. That's what the delivery charges are for, all the power lines and electric poles to your house, all the line workers, the tree trimming, the transformers on the poles, the extra line workers they pay to bring in before every storm, etc. Since only one company provides this service, you cannot change delivery companies.

The supply is the creation of the electricity, it's what pays for the natural gas, solar panels and wind turbines that make the energy. Since anyone can make electricity and put it on the grid, this is what you can shop for. Just watch it, some of those providers are even more expensive than your utility or have long term contracts.