When you take a shower or use any water in your home the drain water goes down the drain pipe and then from there it travels to other parts of the plumbing where it connects to a larger sewer pipe.
When the water reaches the sewer pipe it then travels outside your home and either into the alley or into the street into the main city sewer pipes.
Then after the drain water gets into the main city sewer pipes it then goes into other pipes where it then travels to a sewer treatment plant and then the sewer treatment plant filters and cleans the drain water and then returns the water to the streams or oceans etc.
If you have a septic tank the water from the shower goes into the septic tank and then goes out of the septic tank and into the ground where it's filtered.