Taxonomy is the science of organising everything into like-groups. Scientists classify all living things on the planet. Plants are organised in the Kingdom Plantae.
Plants are organised into four main categories, based upon their phylum, tissue structure, seed type and stature. Phylum refers to the overall type of plant; for example, ferns or flower producers are in different categories. Tissue structure refers to the way that the plant can absorb and circulate water. Seed structure classifies plants by those that produce spores and those that produce covered or uncovered seeds. Stature refers to the overall height and build of the plant; for example, vines and trees vary greatly in their overall stature.
Scientific names are the Latin names that scientists use when speaking about a type of plant. For example, a scientist would call a tall yellow flower Helianthus, but you and I would most likely call it by its common name: a sunflower.
Once you have taught children some of the differences among plants, take them to a garden to show them the differences in leaf shape and structure firsthand. Point out how leaves from a fern differ from the leaves on from maple tree and pine needles. Show students flowers with overlapping petals and examples of seeds that are coated and uncoated.