Young Earth Creationism is the belief that the Earth and the Universe are considerably younger than the age that scientists generally agree that they are (4.5 and 13.75 billion years; more at Ages of the Earth and the Universe), and was created by an intelligent supernatural entity of some kind, usually the Judeo-Christian Elohim-Yahweh or Muslim Allah. The vast majority of Young Earth Creationists (or YECs) in America today are Protestant Christians, and therefore will be the main focus of this article. The creation text is right at the start of the book so people notice it, believers read it and decide it must be true, skeptics also read it and, well get skeptical. That is at least a partial explanation why there is so much trouble between Young Earth Creationists and scientists. 
Christian YECs reject the scientific concepts of the Big Bang, the nebular hypothesis, abiogenesis, and evolution by natural selection, in favor of the belief that the biblical account of creation in Genesis is literally true. They usually rely on calculations like James Ussher's calculation (creation in 4004 BCE) rather than radiometric dating or other scientific methods. They completely reject evolutionary biology and modern geology, and by virtue of that, through a sort of "domino effect", have to defy science in nigh all its forms (eg. gravity) as well.
In addition to the account of creation in Genesis, Christian YECs generally also consider the other main story in Genesis, that of Noah's Ark, to be literally true. This poses numerous difficulties, including the space available on a boat of the size described for water, food, bedding, etc.; how eight people managed to look after all the animals on the arc; and the rigorous definition of "kinds" of animal as they are described in the Bible.
Young Earth Creationists, despite having generally studied non-scientific subjects at university (if they went there at all), often claim to know more geology than geologists, more biology than biologists, more cosmology than cosmologists, more paleontology than paleotologists, and act in most cases like they have a deeper understanding of any given scientific discipline than those who have spent most of their working lives studying it. Generally creationists have to resort to claiming the scientific method in itself is a religion that is flawed, and their hypothesis about a cosmic (in the case of Christians, Jewish zombie) ghost is much more acceptable.
Scientific difficulties with Young Earth Creationism
- The Great Andromeda Galaxy is 2 million light years away. Other galaxies are further away. How did the light from there reach us in 6 thousand years? The YEC response to this is usually to assert without evidence that the speed of light is slowing down.
- Cosmologists have found evidence that the Big Bang happened over 13 billion years ago. Is it likely that so many respected scientists are wrong and a few theologians are right?
- Radiometric dating and other methods of dating suggest that the Earth and Solar System are over 4 billion years old. Geologists see evidence of many different geological processes taking place over millions of years, hundreds of millions of years and thousands of millions of years. Is it likely that so respected scientists are wrong and a few theologians are right?
- "Creation Science 101" by Roy Zimmerman Cool video