Kindergal did a good job of giving you a great overview of IVF vs IUI. The only thing that was slightly incorrect is with an IUI the sperm is actually place into your uterus. With an ICI (inter cervical insemination) where it is put in the vagina, the sample doesn't need to be washed and cleaned because the vagina does all the cleaning for ya. If you have any more questions, let me know!
IUI is a much less invasive and less expensive procedure---Basically, the sperm (after being spun/washed) is injected directly into your cervix at your ovulation time. Many people do IUI in conjection with injectables or other meds.
IVF is when the Dr. retrieves eggs and then takes the sperm and "mixes it with the eggs and then implants them in the uterus.
Again, these are very basic descriptions. You can probalby find much better and more detailed information on line.