An element or chemical element is defined as a substance that consists of only one type of atoms and cannot be further subdivided to simpler substances. An element is characterized by the number of protons in atom's nucleus, also termed as its atomic mass. For example, the simplest element Hydrogen has only 1 proton and hence its atomic number is 1. Oxygen, on the other hand has 8 protons and hence its atomic number is 8.
Please note that elements are not characterized by atomic mass (sum of number of protons and neutrons). An element can have more than 1 atomic mass, all such variants that have the same atomic number but different atomic mass are called isotopes. For example, uranium has two isotopes, U-235 and U-238, etc.
The elements are divided into metals, non-metals and metalloids. Elements are typically presented as a collection known as a periodic table that consists of all the elements known to us (including both naturally occurring and man-made elements). There are over a 100 known elements (118 to be precise, as of April 2015).
Each element is represented by a symbol, e.g., H is hydrogen, C is carbon, U is uranium, etc.
Hope this helps.
I would also just like to add that some elements, such as gold and silver, have been known and discovered for thousands of years already. Other elements, have been synthesized, or created by scientists!
As gsenviro mentioned, all of the known elements lie on the periodic table of elements. Below is an image.
Also, in case you do not know what an atom is, it is what makes up all matter. (Matter, which you should know, means anything that takes up space, even air.) They are made up of protons, neutrons, and electrons. Protons are equipped with a positive electrical charge, neutrons with no electrical charge (don't get confused to think that NEutrons means "negative," remember that it's NEUTRon as in "neutral." Finally, electrons have a negative electrical charge.
I have an amazing video that answers your question perfectly! It's catchy, scientifically accurate and has great animation!
But if you don't want to watch this 3 minute music video, an element is a combination of protons, neutrons and electrons that create an atom. The Periodic Table of Elements show how many protons are found in that atom (ex: Carbon has 6 protons because it is #6 on the Periodic Table). Each element has different chemical properties including if it is flammable, toxic and many other amazing things!
Elements are what makes up you, me and our entire world. Pretty amazing, huh?
Some people confuse elements with atoms
i am going to differentiate between two as
All atoms of given element may or may not have same number of protons
for example hydrogen(element) has three types of atoms protium, deutrium and tritium called the isotopes of hydrogen. they are in different abundance protium is most abundant while tritium is least
similarly some element may have no isotopes at least naturally such as berilium
in such case atom and element is same