How does tap water effect plant growth?

Tap water typically contains minerals and nutrients that are good for plants. Bottled water has these filtered out before it is sold and city water contains chlorine (for example) to help kill bacteria which is harmful for plants.

The "tap water" differs in different parts of the world. Countries in tropical areas have chlorine (and sometimes fluorine) added to it to kill and control bacterial (and fungal) growth. These elements in high concentrations can have detrimental results to plant growth and seed germination

Think practically. About 99.9% of all indoor plants IN THE WORLD are watered with tap water; about 90% of all domestic gardens and landscapes are watered with water that originates basically from a tap.