Big groups: incase a portion of your sample doesn't work, dies, is corrupted or something of that sort occurs you have more samples too obtain results from.
Identical or similar groups: this is essential since results can be manipulated by external conditions and if they vary for different groups, results aren't accurate.
Same conditions: assurance that other environmental factors do not influence the response/results.
Control: for comparison and set standard.
I think....
Yep, you're essentially there with most of it!
Big groups: this is to deal with the effect of randomness. So if you think about if you were doing a study on whether a drug causes heart attacks. You have a group of two people. One gets the placebo, the other gets the drug. The one with the placebo has a heart attack a week later and dies. What might you conclude from this study? You may conclude that the drug actually
prevents heart attacks. I'm sure you can see why this conclusion is a little bullshit...there are any number of reasons why that person suffered a heart attack. So, by having larger groups, you help to reduce the effect of random events like that. Because if you've got really big groups, a random effect in one group is likely to be replicated in the other group. The bigger, the better group wise!
Identical/similar groups: when you're conducting an experiment, you want to draw a relationship between two variables (i.e. you're trying to work out whether A causes B). By making the groups identical, you limit any other factors that could cause the result you're looking for. E.g. if you're looking at whether a drug causes people to lose weight, and you put obese people in the weight loss group and skinny people in the control, then you've pretty much stacked your study...of course the obese people are going to lose more weight, they have more weight to lose!
Same conditions: same as identical/similar groups; to make sure that nothing interferes with the results
Control: exactly what you said, it's a standard against which one can compare a result.