There are some groups of medications that should never be combined with alcohol. It's hard to list them all but the ones that come to mind are sedatives (antidepressants), central nervous system depressants, pain killers and seizure medications.
Like the article said, barbiturates are central nervous system depressants and they also help prevent seizures. So they're one of those groups of drugs that should never be used with alcohol.
Alcohol is also a central nervous system depressant although few people are aware of this. So taking alcohol with barbiturate will cause a greater affect on the nervous system. This doesn't just mean that the person will be drowsy and sedated. This also means that breathing, heart rate and decision making will be affected. The biggest risk is that this combination might slow down breathing to such an extent, that the individual may fall unconscious and even die.