The Jewish holiday of Passover is approaching. Just like any other Jewish holiday there are many restrictions for the Jews such as not working or planting. However, on Passover there are many additional restrictions pertaining to what a Jew is allowed to consume. These restrictions are that a Jew is not allowed to eat chametz or have chametz in their possession. Chametz is anything made from the five main grains including wheat, rye, barley, spelt and oats unless it was unleavened and cooked under eighteen minutes, in which case it is called matzo. (Watch the process of baking matzo here.)
Because of the extreme importance of keeping these restrictions many Jews have taken on additional restrictions which are looked at as an extra fence to prevent a Jew from breaking the main restrictions. On Passover many Jews have taken upon not to consume or own kitniyot just like chametz. Kitniyot means legumes but incorporates all the other additional restrictions such as corn, rice and beans. Back when the kitniyot restrictions were made the Jewish people were in a state of diaspora and in many different countries. Only the Ashkenazim made the extra restrictions of kitniyot. Ashkenazim come from countries such as France, Germany and some eastern European countries. However, Sephardim did not impose the extra restrictions of kitniyot. Sephardim come from Spanish and Middle Eastern countries. The Ashkenazim and Sephardim thus lived in different places and had different leaders. Hence, the difference in customs.
There are many differences in opinions of why the kitniyot restrictions were made. Some say that it was because foods such as rice and beans can be made into flour and bread and therefore be mixed up with the five main grains which constitute chametz. Others say that it was because these foods were typically stored together with the five grains and were therefore worried that it might be mixed together with chametz. There are also many variations of what is considered kitniyot. Some believe that any foods that were not known of back in the times that the additional restrictions were made are considered kitniyot. So, for instance tomatoes were not a prevalent food in those lands in that time. Therefore, some Jews say that tomatoes are considered kitniyot. However, most Ashkenazim do not follow this way of thinking.
Even though it was mainly the Sephardim that did not impose the kitniyot restrictions many Ashkenazim today also do not restrict themselves of kitniyot. Some Ashkenazim here in America and other places do not restrict themselves. However, it is mainly in Israel that many Ashkenazim do not restrict themselves of kitniyot. (See why here). Also, many Ashkenazim that marry into Sephardic families adopted certain customs such as not to restrict kitniyot. The main reason why some do not restrict themselves from kitniyot is that they feel like such a restriction is not necessary or that the additional restrictions were only needed in those countries and therefore does not apply to them. (Also see recent responsa on the controversy of the restriction.)