Compounds and mixtures are easy concepts to understand. Chemically the difference between them lies in their atoms and whether the atoms of different elements are chemically joined (compound) or just mingled (mixture) together. This chemical difference affects how compounds and mixtures may be separated back into their constituent parts again.
Elements - as found in the periodic table - are of course the simplest substances that exist. They cannot be broken down any further and they consist of just one type of atom. Commonly elements are divided into different groups, like metals and non-metals. Elements sometimes combine together with other elements to form new substances - and do so either as compounds or mixtures.
When elements combine chemically to form compounds they cannot be physically separated again. For example, the elements Hydrogen and Oxygen combine together chemically to form water (H20). There is a chemical bond between the atoms of hydrogen and oxygen that mean the compound cannot be broken down by physical means.
If water is to be separated back into its constituent elements a chemical process is necessary. In this case electrolysis, heating the water, will allow the atoms to separate again into the base elements. A process of reduction gives electrons from the cathode to form Hydrogen gas. There is no simple physical separating of elements.
When elements (or elements and other compounds) combine physically to form mixtures then they can be physically separated again. For example, salt (sodium chloride, NaCl) and water (H20) are compounds that combine to form a mixture called salt water. There is no chemical binding of atoms and the mixture can be broken down into its constituent parts again by physical means.
If salt water is to be separated back into its constituent parts then a simple physical process will suffice. Salt water can be left to evaporate or boiled away to leave behind dry salt. Allow the evaporated water to condense on the lid of a pan and drain away into a container and a physical process has separated the two components.
Sometimes a distinction is made between mixtures that are homogeneous with the constituents evenly spread throughout the mixture and mixtures that are hetreogeneous with constituents lumped together in different proportion in the mixture. And there are mixtures that are colloids being hetrogeneous mixtures that appear uniform.
Mixtures (Purdue University's simple explanation of mixtures and compound) tend to retain the properties of its components while compounds can have very different properties to its constituent elements. However, the ability to separate mixtures by physical means and the chemical bonding of the atoms remains at the heart of the difference between compounds and mixtures.