If an experiment is conducted in order to assess the effect of a changing variable both a treatment and control group are needed, the first group receives the treatment and the later does not. Individuals have to be randomly sent to one of the two groups
In this example the treatment variable is a dicotomic one: wash the wound with honey (=1) or not (=0). We want to asses if it affects negatively the probability of getting a would infection. It is necessary to rule out other factors that can affect this probability, other than the treatment variable, such as the healthcare access, the hygene conditions, the family income, the number of siblings, etc. This is why we need two groups, because the control group is affected by all the variables except the treatment, and the treatment group are affected by all variables (including the treatment). Hence, the final conclusion on the effect of the treatment is reached by comparing the results in the two groups.
If there is only one group, there is not a random assingment of the treatment whose effect we want to quantify and therefore the results will be contaminated by a selection bias.