First off, arsenic is a naturally occurring metallic element. It is present naturally in soil and water. Any plants or animals that use the soil and water can then contain small amounts of arsenic.
Unfortunately water or soil that is polluted by arsenic laden fertilizer or other sources of arsenic have much more arsenic in it than normal. A crop like rice that grows in flooded land has the opportunity to soak up more arsenic than a crop that does not grow in floods.
So the problem is that while arsenic is naturally in the soil, humans have managed to pollute with even more arsenic. For US consumers this is especially important for rice grown in Arkansas, Louisiana, Missouri, and Texas. These fields formerly grew cotton. A pesticide that used to be used to kill boll weevils contained arsenic and remains in the soil.
Other countries may have their own "hot spots" where rice is more contaminated than others.
One thing that can help is to rinse rice carefully before preparing. Then use 6 cups of water to 1 cup of rice. That is a much higher ratio than you are probably used to. After the rice is cooked, drain it. You will lose some vitamins this way, but you will also lose some arsenic too! According to Consumer Reports that gets rid of about 30 percent of the inorganic arsenic.