"Real fear" refers to feeling genuinely scared or afraid, as opposed to just a mild or imagined fear. It describes a genuine sense of danger or unease that a person experiences in a situation. Full definition
Nearly everyone I approach is wary of speaking with me because of very real fears of political repercussions or criminal retaliation. (scientificamerican.com)
The combination of this pessimistic anthropology, the very real fear of hell for themselves and others and cultural values supporting harsh discipline made for a dangerous combination for children. (religion-online.org)
Another very real fear for second time mothers is that there just won't be enough love to go around. (pregnancy-info.net)