According to Malthus, food and other resources are limited, and a population growth that exceeds a certain pace will inevitably hit a resource ceiling, and will result in decreasing standards of living, poverty, conflict over scarce resources, famine etc. (This is called a Malthusian catastrophe). Ultimately, population growth will halt because if this, and population levels will return to the “normal” equilibrium possible within the limits offered by nature (the so-called “carrying capacity”).
And if these disasters aren’t enough, active population control is necessary, including measures such as the abolition of social security (social security doesn’t incite people to birth control, see here) and even more extreme policies (many of which proposed by Malthus’ more enthusiastic followers rather than by himself).
Malthus agreed that humanity was capable of increasing its productivity, but believed that population growth would necessarily outpace this increase. The facts are, however, different. Standards of living have risen enormously over the last centuries, notwithstanding large increases in population numbers. GDP growth has even been faster than population growth, giving, on average, every human being more resources than ever before in history. Of course, these resources aren’t equally distributed, but that’s a problem of justice, not of population.
Blaming everything on overpopulation is simplistic. All major problems in life are multi-causal, and population isn’t a real or major cause in many cases (bad governance is often a more important cause). And when it is, population control isn’t the answer. Technology, productivity, consumer adaptation, better governance etc. are more promising solutions.