A repeated measures ANOVA involves any situation where you measure subjects two or more times on the same test. So you can imagine many situations where this would occur. Imagine you want to track children's' progress in reading ability as they go through school. Each year, the children are asked to read as many words as they can, and are stopped when they read 5 words in a row incorrectly. You could give a group of children the same reading test in Grade 1, Grade 2, and Grade 3. Since you are measuring each child repeatedly on the same test, and since you are measuring them more than two times, you have to enter the data into a repeated measures ANOVA.

For a factorial ANOVA design, you are measuring two or more groups on a test, but you are only measuring each individual one time. You are then comparing the groups (of different people) on their performance on the task. To run a factorial ANOVA, you could ask a similar question to the one above, but test it using a different design. Investigating how children progress on their reading skills between Grades 1 and 3 is a good question to ask, but it takes a long time (and lots of researchers and money) to collect the data for three years. So, if you want to save a bit of time and money, you could test Grade 1, Grade 2, and Grade 3 students on the reading test used above. You are essentially doing the same thing as above, but you're using different children in each grade, instead of following each child through the three grades. (This is a cross-sectional design; the repeated measures design was a longitudinal design).

Now, you need at least 20 people per cell for this study. You are measuring children from three different grades, so you need 3x20=60 subjects for this experiment. (Think about how many you would need for the repeated measures study - you are measuring the same children three times, instead of measuring three different groups of children one time).