Although the former posting regarding basics of FMLA is accurate, I have to disagree with the statement regarding intermittent leave (unless I misunderstood the intent of this part).
As the former replier stated, the FMLA is for "serious" health conditions - this is not meant for situations such as the common cold,flu, etc... Unless the absences to care for an ill child on an intermittment basis is directly tied into the child's "serious health condition" (i.e., ongoing treatment, etc.forsuch), the employer cannot count that leave as FMLA.
Intermittment leave is allowed under FMLA if it is for continuing care for a serious health condition. Remember that the employer can require a "Health Certification" from a medical provider that states the situation is a "serious health condition." This "intermittent" leave can and should be counted toward the 12 week per 12 month FML allowance for "eligible" employees.
Keep in mind that your employer must notify you appropriately regarding if and when leave will be counted as FMLA. Employers cannot deem leave as FMLA retroactively when they realize that they did not properly notify you. On the other hand, you also have an obligation to notify your employer of the situation in a timely manner.
I hope that helps.