Primary research is defined as factual, first-hand accounts of the study written by a person who was part of the study. The methods vary on how researchers run an experiment or study, but it typically follows the scientific method. One way you can think of primary research is that it is typically original research.
For example: Going back to our original example of the literature review on the effects of animals and stress, we need to determine what kind of research we will include in our write-up. We go online and start collecting articles about stress and animals. There are probably a lot of them, so we begin to sift through them. When sifting through the research to locate what we want, an easy way to locate primary research articles is that they will be written by a researcher who conducted the study. For instance, a researcher examined the stress hormones in people who owned cats, dogs and no pets. Another researcher looked at the stress people say they have and how many pets they own. In these examples, a researcher is examining and writing about the study they conducted.
