Derek Thompson has a good piece on the difficulties and ambiguities of measuring online readership. But I think the only way to understand this correctly is to start with the near-impossibility of measuring analog readership.
Typically an analog magazine won't even try to measure readership of its offerings. It will instead offer subscription figures. But knowing how many people subscribe to Time gives us almost no information about how many people read Time. An issue in the waiting room of a doctor's office might be read by many people. Issues delivered in the mail to households might pile up on the coffee table. A household might have two or three enthusiastic readers of the magazines it subscribes to. Or one enthusiastic reader and another person who picks it up from time to time since it's there. The best you can do is count up all the adults living in all the households that subscribe and say that this is a kind of upper-bound on your readership. You know that not all of those people read your magazine, but probably the vast majority of them at least see your magazine and might read it.
But not only is there a huge error bound on this kind of guesstimation, it's not at all informative about the interesting questions you might have about a magazine's readership.
A writer, for example, would probably like to know which of her articles are popular. And her editor would probably like to know as well. On the one hand, it's good to write about subjects that people are interested in. On the other hand, it's good to put in the work to make people interested in the most important issues. But subscription data doesn't tell you anything about this.
An advertiser, meanwhile, is going to want to know how many people are likely to see any particular advertisement. Circulation numbers just don't tell you about this. Clearly all else being equal if Magazine A has double the subscriber base of Magazine B, an ad in Magazine A is likely to be seen by more people than an ad in Magazine B. But "all else being equal" is doing a lot of the work here. How long are the magazines? What is the actual behavior of the readers?
On digital, the problem isn't so much that the audience is harder to measure as it is that you're going to get more arguments about it. With analog, you have basically two numbers—paid subscriptions and newsstand sales. The numbers aren't very informative, but they are unambiguous. On digital, page views gives you valuable information. Monthly unique visitors gives you valuable information. Different measures of dwell time and sharing also give you valuable information. All told, a thorough battery of digital statistics probably gives you a much more accurate and more nuanced portrait of readership than old analog stats did. But because there are conflicting pieces of valid information and a bunch of money at stake, you also see more arguments about it.