First, there seems to be a taxonomic usage of the term "macroevolution". Opponents of evolution are often using the term as a proxy for folk taxonomy. Dogs, cats, spiders, ants, birds, snakes, human beings, monkeys, flowers, etc. are all taken to be macroevolutionary units because they all correspond to an uninformed folk taxonomy that we learned as children.
You often hear them say things like "nobody has ever seen a dog evolve into a cat" or whatnot, in which case macroevolution is presumably equivalent to the diversification of new Linnean families; but when talking about less familiar groups of animals, I have often heard things like "yes but it's still an insect isn't it?", in which case macroevolution is taken to be equivalent the diversification of a Linnean class! On the other hand, talk of human evolution will resound with "the missing links between Australopithecus and Homo", so in this case macroevolution is the diversification of a genus.
I'm afraid there's no sense to any of it, because it's taxonomy by people who aren't sufficiently motivated to inform themselves about classification. Hence we hear both "it might have microevolved, but it's still a monkey" and "it might have microevolved, but it's still unicellular" in the same breath!
An alternative usage is in terms of biological structures. Microevolution is taken to be molecular evolution and the evolution of proteins, while macroevolution is taken to be the evolution of body parts (especially tissues and organs) or body plans. So we often get "how does evolution create hair/wings/hearts/brains/eyes/larvae/sexes" etc. The distinction probably has more merit here; I can appreciate there may be a conceptual difference between "tweaking" an existing metabolic pathway and evolving a new limb. In general it boils down to the idea that microevolution is the modification of a single modular trait, while macroevolution is the coordinated evolution of multiple traits or the origin of new "modules" which change the systematic functioning of the organism. So, the evolution of the ability to hold breath for a long time is microevolution, the evolution of a hand into a flipper is microevolution, the evolution of specialised hemoglobin is microevolution, but the evolution of an aquatic lifestyle from a terrestrial ancestor is "macroevolution" and impossible.
Finally, they often just mean "microevolution can be observed in a lab experiment, while macroevolution cannot". So microevolution can be observed in real-time and in living organisms, while macroevolution must be inferred (for example from fossils, systematics, or whatever). The attack on evolution then amounts to an attack on the validity of scientific inference.