Elements themselves are not crystalline or amorphous. Instead this describes the structure of certain elements and compounds in the solid state. For instance, a single element can be found in both a crystalline form as well as an amorphous form.
A crystalline solid is one in which there is a regular repeating pattern in the structure, or in other words, there is long-range order. In fact, you can completely describe the entire crystal by describing the single "repeat unit." For instance, as a simple example, if I have the pattern ABCABCABCABCABC... (that repeats infinitely) I can completely describe it by just saying it is "ABC" over and over again. In a 3-dimensional crystal, this repeat unit is called the "unit cell." Some crystalline solids are diamond, table salt, and many types of minerals found in the earth.
An amorphous solid is one which does not have long-range order. In other words, there is no repeat unit. To contrast the example above, it would now be: ABCBCABBCACBACBAC... where there is no way to figure out what will be the next letter. Some examples of amorphous solids are glass (in windows, for example), wax, and plastics. If a liquid cools very quickly, the molecules will not have time to arrange themselves in the most favorable pattern (which will almost always be crystalline), and so they are locked into a disordered solid.
Silicon is a common solid that can be found in both amorphous and crystalline forms, depending on how it is manufactured. Crystalline silicon is much harder to grow, but it is what is used in computer chips. Amorphous silicon is much cheaper and easier to grow, and is commonly used in solar panels.