Source: Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2012 Revision http://esa.un.org/unpd/wpp/index.htm
The conditions that create slums are too complex to summarize completely, but it is possible to see commonalities in the forces driving these phenomena.
First, population growth in many developing countries is increasing at unprecedented rates that are difficult for many to comprehend in scale. For example, Nigeria's population could very well eclipse China's before the end of this century.  This amounts to over one billion people living within an area just larger than the US state of Texas.
This growth is happening almost entirely in cities. This rate of urbanisation from rural to urban stems from a variety of factors: climate change, political and cultural forced displacement, or economic imbalances.
Rising Intermediary Cities and Other Factors
We may think that mega-cities like Lagos or Kinshasa are experiencing the most growth. But actually intermediary cities are seeing the highest rates of growth, as many migrants are finding mega-cities too expensive, too congested or too far from their home base.
But rural-urban migration is not the sole contributor to the urbanisation phenomenon. Urban In-migration, or internal population growth, as well as municipal incorporation of peri-urban areas are also driving much of the surge.
Generally, these three factors (rural-to-urban, in-migration, and peri-urban incorporation) are significant contributors to the urbanisation rates we are witnessing today, and are expected to accelerate further in the future.
Why Do Slums Form?
The Housing Value Chain
Source: UN Habitat 2012
Urbanisation is not the only contributor the rapid rise of urban informal settlements. The institutional and physical systems in which migrants arrive are insufficient or outright non-existent. In the absence of comprehensive urban planning and land policy, it is oftentimes a few power-groups, or dominants, who are developing cities, oftentimes to their own interests. This leaves systemic gaps for the vast bulk of society, including the middle classes as well where even professionals struggle to afford housing.
During the colonial era, government urban planners
anticipated a few hundred thousand residents in the administrative capitals and major trading centers. Built with the purpose of extraction for the mother country little priority was placed on long-term planning cycles.
However, in the post-colonial period, nascent nations seeking local development were ill-equipped for such an influx into urban centers, amidst a multitude of other challenges- both internal and external.
Relative to rural areas, urban areas inherently require a higher degree of infrastructure and social organization, transport mobility- not to mention centralized utility distribution networks, knowledge capacity and legal enforcement mechanisms.
Building such infrastructure in the midst of a swelling population influx is like trying to build levies during a torrential flood!
Nairobi, Kenya in the 1950s, Approximate population: 80 thousand.
By 2050, Nairobi's metro area is expected to reach 14 million.
If we examine the Housing Value Chain, we see that the actual construction of houses is just one of twelve main components of a healthy housing market.  If the conditions at the macro-level are not properly established, the contiguity of all players at lower levels cannot properly 'fuse' to serve all population segments.
When governments cannot (or do not) effectively establish land-use policies, regulatory frameworks, urban planning and land markets, development is relegated to the elite few with the political and financial means to 'go it alone' and carry out each step independently.
For example, private sector developers mainly serve the highest income markets. This is largely because these segments provide adequate returns for the high costs of construction and severely high interest rates, as banks must lend in relatively small mortgage markets, not to mention high-inflationary economic climates with high currency volatility.
For example, in the Democratic Republic of the Congo, where the lowest cost private developer house averages $25,000 USD, only 0.3% of the population can afford such homes. This scenario is more the norm than the exception, as less than 10% of all Africans can afford the cheapest private developer house in their countries. 
Number of housing units to be built every day from now until 2030 to meet global demand.