When you mix two liquid chemicals together, they are usually dissolved in a pool of water. The solid chemical powders naturally break apart into floating electrically charged particles called ions. Some of these floating ions bump into each other and immediately lock together tightly.
They form a brand new solid chemical that sinks directly to the bottom of the flask. This newly formed solid chemical product is scientifically known as a precipitate. However, not every single ion in the watery beaker gets involved in making the new solid.
Many of the floating particles simply watch the entire reaction happen without changing their form at all. Chemists cleverly refer to these completely uninvolved pieces as spectator ions. If you write down everything in the beaker, the chemical equation becomes very long and confusing.
To fix this mess, scientists cross out the spectator ions from both sides of the written equation. The shorter leftover equation is properly known as the net ionic equation. It highlights exactly which starting pieces actually combined to build the final chemical product. This simplified version makes it much easier to balance the math and understand the core chemistry.