The simple answer is that it makes their life easier.
Imagine you're a recruiter. One half of your job is to grind through hundreds of resumes every week and organise them somehow. It's easier to do that if you can use the same program to view every resume, and most businesses{1} use Word. Back in the day this was a defence again people using specific versions of specific programs ("can only be opened using AbiWord 2.1 or earlier"), but these days it's as likely to be a defence against cryptography (signing or encrypting).
Remember that in more graphic-oriented industries people will submit everything from "video resumes" to flash files. It's not uncommon for architects, for example, to be asked for a "resume" that's A3 or larger as well as a portfolio. Submitting that digitally as well helps everyone a great deal (although it does raise the question of whether people even know what the word "resume" originally meant. Viz, a summary document)
Inevitably there will be a database somewhere (at worst, the MS-Outlook email "database"), but more likely some kind of recruiter tool. Many of those can only import a limited range or file formats, and a lot cannot cope even with password-protected Word files, let alone the various encrypted and signed formats offered by PDF and other, more capable file formats.
{1} for some value of "most" that varies with location and industry.