A commenter has asked me why we study microeconomics and macroeconomics* separately. It's necessary but not sufficient to simply say that microeconomics is the study of households, and firms**, and macroeconomics is the study of the national economy as a whole. After all, while physicists do specialize, we don't have "microphysics" and "macrophysics" as separate disciplines, even though physicists study everything from quarks to planets to galaxy clusters to the whole universe. It's all just physics.
*There are actually three levels of economics: micro, macro, and international economics.
**Households and firms usually are not internally organized by markets, although there are many economists who use economic techniques to study intra-household and intra-firm behavior.
Economics is different because economics is more complex (has more independent "moving parts") than physics, and has more feedback mechanisms. Specifically, although they are connected, there are features about the economy as a whole (macro) that have such a radically different character than features about the economy of individuals (micro) that we must think about them in radically different ways. A more apt analogy is the difference between biology (the study of individual species and organisms) and ecology (how organisms interact). Obviously, ecology is intimately linked to the biology of the species, and in some sense emerges from that biology, but the conceptual tools are very different between the two fields.
Economics in general is the study of trade-offs. When someone has to give something up to get something else, economists spring into action! The fundamental difference, therefore, between micro and macro is what is being traded off, and how those trade-offs are measured and conceptualized. Fundamentally, microeconomics is about relations between actors in a national economy, but there is nothing for a national economy to be relative to. (Again, international economics complicates this framework a bit, but by and large, most large national economies such as the United States can be treated as closed systems with a small correction for net imports and exports.)
The biggest difference is flow. Micro is linear: a household or a firm has an income on one side and an expenditure on the other side, with stuff coming in or out in the opposite direction. In contrast, macro is circular: money circulates between households and firms, with labor and stuff circulating in the opposite direction.
Another difference is money. A household or firm can run out of money; the national economy cannot run out of money. While some individual household or firm might not have money (savings or income), and is therefore limited in what they can consume, the money is always somewhere in the national economy. In micro we study how households and firms allocate their money, how they make choices constrained by the money that they have (savings) and that they expect (income). In macro, however, because the money is always somewhere, and the total amount of money is (more-or-less) constant, so we don't conceptualize trade-offs as being constrained by money. Instead, macroeconomics is concerned with the total real productivity and consumption of the economy. Indeed, there is presently a debate between classical/neoclassical macroeconomists, who think that money doesn't matter at all (it's just a lubricant; you have to have some, but adding extra lubricant won't make your engine any more powerful), Keynesians (classical, neo- and paleo-), who think that money does matter (prices not as much), and monetarists, who also think that money and prices matter, but in a different way than Keynesians. In contrast, there are exactly zero microeconomists who think that the money a household or firm has doesn't matter.
Similarly, individual households want to accumulate money. They want to optimize their money income and/or their profit. In macro, however, we can't make a profit; profit is always relative; the net profit for the economy as a whole is exactly equal (as a boring accounting identity) to whatever new money we have put into the system in one way or another, i.e. mining gold and silver or printing dollar bills.
Another difference is what is being traded off. In micro, we trade off between production or consumption of different items. I can buy better food, or I can pay more in rent. I can choose between oranges and apples. A household can work more or have more leisure. A firm can produce more or fewer oranges or apples, and it can choose between more capital (machines) or more labor. In macro, however, all there is is one big lump of everything; generally, we don't worry about the trade-off between everything and nothing (nobody wants nothing). Instead, the big trade-off is between consumption, producing stuff we'll use today, and investment, producing stuff that will produce stuff we'll use tomorrow. In macro, we also think about trade-offs between the the large-scale entities in an economy: all households (and sometimes all working households vs. all investing households), all private productive firms, all financial firms, and, of course, the government.
There is also a controversy in macro as to whether the economy as a whole can fail even if all the parts are working correctly. Classical and neoclassical economists say that if all the parts (households and firms) are working, then the whole economy is working by definition; if you don't like how the whole economy is working, then one or more of the parts are failing. For example, the classical economists attribute the Great Depression (and the current Lesser Depression) to a combination of malinvestment (we built too many factories to make stuff people didn't want), structural unemployment (workers didn't have the skills that firms wanted), irrationality (workers refusing to accept lower money wages even though prices had fallen, so their real wage had increased), and government misregulation (in the extreme, some assert that all government regulation except enforcing contracts is misregulation). Monetarists lean towards the classical view in this regard: they attribute problems in the whole economy to failures of the banking system or government regulation of the banking system. In A Monetary History of the United States, Milton Friedman and Anna Schwartz make a compelling case that errors by the Federal Reserve in regulating and supporting the private banking system at least deepened and may have caused the Great Depression. In contrast, Keynesians assert that all the parts of the economy can be working correctly in micro terms, but the economy as a whole can still fail, measured by cyclical or involuntary unemployment.
Again, in contrast, there are exactly zero microeconomists who claim that all the parts of a firm can be working correctly, it has sufficient capital and labor in the optimal proportion, it has a market for its correctly-priced product, and its workforce and administration are competent, and yet the firm can be unprofitable.
So, basically, the individual household and firm are conceptually very different from all the households and firms in a national economy. Therefore, we divide up economics into micro and macro.