My first reaction is that this is really good for everyone.
For Verizon, as they aptly spun it, it allows them to focus on their core business. I'm not in Media or Telecom, but from the outside looking in, the synergies between those two segments aren't obvious.
For Yahoo / AOL / Verizon Advertising, these can be repackaged into sets of assets that "make sense" so that they may be sold to strategic buyers and ultimately have a better home than being the ugly duckling in Verizon's portfolio.
For Apollo, the benefits are obvious. There's probably lots of operational improvements to execute on, again due to the fact that Verizon was likely not really focused on these businesses. Presumably the fund will reap huge returns if they can deliver on these improvements and exit successfully and timely.
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EDIT: There is one more nuanced question I forgot to address: is this "really good" for the employees to? On an individual scale, probably not. I'm sure many people will be let go once Apollo is at the helm. But from a broader view, it is arguably "good" for everyone collective in the long run. Verizon really can't do much with the asset, so the alternative to selling is letting it wither away in the hopes of some miracle, with the more likely outcome being that Yahoo and AOL would become even worse shadows of their former selves with each passing day.
Eventually people would be let go anyway and those businesses could be shut down unless some miracle strategic buyer (i.e. not a private equity owner) came along and bought them. But most strategic buyers are not comfortable buying bad operations and turning them around. They find it too risky, so that's usually a job left to financial sponsors like Apollo who are built for that. In fact, these days most PEs are not even interested in turning operations around because they also find it too risky—and sponsors learned they can make more than enough money by just being great at finding sub-scale / non-core assets, putting them together in a "platform" and selling them to another sponsor or exiting through an IPO.