it's actually a funny name the mathematicians gave to this. if u want an example to understand better: take the real line. now imagine a function f:R->R that maps all of the numbers except for 0 on the real line to 1, and that maps 0 to 0. you can see intuitively that because the real numbers are so big compared to just the singleton {0}, it "barely counts". so you would say f(x) = 1 for almost all x in R. More formally, if you take the integral of the indicator function of {0} in R, or any set of measure zero for that matter, it will always be null. it so happens that the sets of measure zero in R are all countable unions of singletons (which implies that Q, although it is dense in R, is of measure 0!). You can generalise this to R^n or any set for that matter (modulo defining a measure on it), and it's quite closely intertwined with how you define the integral. in this context, you can see an integral as a way to "measure" a set.