For many years, the raster image processors (RIPs) used to create negatives or plates for plates presses used Postscript. The problems with Postscript were that files were huge and it had no way to recognize or handle transparency.
By the late 1990s transparency was everywhere. Blend modes, drop shadows, glows, opacity settings are all examples of transparency effects that might be in a layout, but if they couldn't be expressed in Postscript then they couldn't be printed. The answer to this was Flattening, which "adds up" all the effects of transparency and rasterizes any regions of the document where they are applied so that the appearance is maintained, even though the actual structure isn't.
After Acrobat and PDF were introduced, PDF became a big hit with the printing industry. A PDF was much smaller than the equivalent Postscript file, making it easier to transmit and requiring less memory in the RIP, and it was non-proprietary: Adobe essentially gave it away. Anyone could take the specification and create their own PDF reader, processor or converter without paying a license fee to Adobe.
In theory, any flavor of PDF should produce predictable output, but with other companies than Adobe creating their own PDF engines, things got messy. Adobe worked with the big press manufacturers and various standards bodies to create an international standard PDF format that would be compatible with all RIPs and produce predictable output on press. That was the first of the PDF/X standards, which we now use as PDF/X-1a.
Designers and printers like standards like this because they don't like surprises on press. Surprises always cost, and can be hugely expensive.
The internal format of -1a is Acrobat version 1.4, which does not recognize transparency. A PDF/X-1a, therefore, has all transparency flattened. It is the simplest PDF/X format, the oldest, and therefore the one that you can pretty much guarantee is compatible, no matter who runs the press. A printer whose prepress department can't handle PDF/X-1a is one that you definitely want to avoid.
Once transparency has been flattened it can't be altered accidentally by some over-excited intern in the prepress department or messed with by the RIP software, so PDF/X-1a is often referred to as the "safe" PDF output setting. Almost all the work I send to press is in this format, and I have yet to receive an unpleasant surprise.
Later standards such as PDF/X-4 do support transparency, because technology moved on and Postscript was becoming increasingly obsolescent. The most modern RIPs are able to process a PDF directly to film or to plate without conversion to generic Postscript at any point in the workflow, which speeds up and simplifies the process of getting stuff printed. Not every printing house is equipped with the new type of RIP, though.