Primary, Secondary, and Tertiary refer to how close the info source is to an original source, whatever that may be. There are pros and cons to each, and the best research takes a mixture of primary and secondary sources, whereas tertiary sources are part of your pre-research process.
Primary sources are original data -- documentation of an event itself, so to speak, rather than interpretation of it. In history, this means letters or diaries and so on. In science, this would be reports of empirical research. In government, the text of laws and statutes are primary sources.
We use these because: they're the originals. Whatever we're looking at, this is straight from the horse's mouth.
Limits for this type: Not placed into a context.
A secondary source is a layer removed from the primary source. The historian reads several diaries and writes an article about an event based on the different points of view. A political scientist or a journalist writes out the implications of a statute.
We use these because: (generally) they contextualize the primary sources, or they provide incredibly current information (i.e. news articles).
Limits for this type: Variety of viewpoints at play in interpreting and applying the primary sources. Authors may be trying to interpret subjects they aren't well-versed in.
Tertiary sources are yet another layer removed from primary sources. They have a specific niche, and can be helpful, but you don't usually see these actually cited in academic literature.
We use these because: They can assist with research, either by helping to introduce a topic or by steering you to primary or secondary sourctes.
Limits for this type: General information, filtered through extra people
If you're looking for...
These can honestly come from anywhere: your research will cumulatively build on itself, and anything can be inspirational or insightful. That said, there's definitely some better places to get started.
This is where scholarly sources really shine: they're nothing but deep dive. (Though in the case of journals -- not every part is scholarly. Back and Front Matter and Book Reviews are a couple common sections that are more tertiary.) Use the library databases foremost to locate. Other options: Google Scholar, ResearchGate, inter-library loan requests.
Depending on your topic, there may be in-depth news reporting on the subject.
Books can be pretty good at this, too, and surprisingly overlooked!