Let's consider a simple example. Imagine a small, metal, well-polished rod, about 1/16" in diameter and 1" long. Now, imagine that we have about 500 such rods and we arrange them in parallel so that they float next to, and easily slide by, one another. We have created a well known toy that makes what is called "metal pin art". If you press your hand, or any object, against one side, its topography will be transferred to the other. The collection of pins (a system) has a property that no single pin has. That property is the ability to create a representation of things pressed against them; in other words, image creation. That property is not present in any individual pin, but "emerges" from the organized collection of metal pins. Another simple example. We start with a single tone. It has a frequency, loudness, duration, etc. Now imagine we have a large collection of assorted tones and we organize them in such a way that a song emerges from the collection. While the song arises from the collection of tones, it is distinct from any individual tone. If we organize the same set of tones in a different pattern, creating a different set of relationships, we would get a different song. In both of these simple examples, we can easily detect the constituents from which the new property emerges: we can still hear the individual tones and see the individual pins.
Next, consider a slightly more complex situation, one in which we cannot see the players, the constituent units, even before we restructure them in a new way. For example, what happens when we force two gases, hydrogen and oxygen, to combine to make water? We certainly cannot see or hear either constituent gas in the newly created water. Why not? It takes a few steps to answer that. To the best of my knowledge, chemical properties emerge from the organization of protons, neutrons, and electrons along with their associated immaterial fields. That means the macro properties of our starting gases are already the result of emergence from more fundamental bits of reality. When hydrogen and oxygen combine, their atoms are rearranged to create new electron fields across the molecule, and it's that new emergent structure/pattern that creates the new properties of water. The basic constituents — protons, neutrons, and electrons — are a few layers down from the macro level we see, and are thus hidden from our casual observation.