I'm not sure whether that sentence from the article actually makes sense. But to answer your question more generally: you start with some model, with one or mo

I'm not sure whether that sentence from the article actually makes sense. But to answer your question more generally: you start with some model, with one or more parameters for which you don't know the value. e.g. "the galaxy contains N uniformly spread out interstellar objects that are big enough to see if they happen to come within 1 AU of Earth." Then we start watching the sky, and after 10 years we see 1 such object. Then for each possible value of N, you could calculate the probability of observing exactly 1 such object during a decade. One particular value of N is going to give us the highest likelihood of getting that result. We call that value the "maximum likelihood estimate" for N.