If a soil cannot absorb the amount of rainfall that is falling on it, what happens to the water?

Soils have the capacity to absorb water, which is commonly known as infiltration rate.
However, this capacity varies according to the soil's components. The components are sand, silt and clay, which are expressed as a percentage. Soils with a high content of sand are called light or sandy soils, and they have a very high infiltration rate (IR). In other words, they have a high capacity to absorb water. Those soils with a very high clay content, are called heavy soils and have a low infiltration rate.
Also, the water absorption capacity (or infiltration rate) is determined by the initial water content within the soil. If a soil is at its maximum capacity for water absorption is a dry soil, and could be at the Permanent Wilting Point (PWP) when plants can not get water from it. On the other hand, a soil with all the pores filled with water is a saturated soil. In this last situation, the soil water absorption capacity is zero.
Slope is another factor that has influence over the infiltration rate. Soils with a very steep slope, have a low IR.
According to the above expressed, if a soil cannot absorb the amount of rainfall that is falling on it, because of its steep slope, the water will cause which is known as rainfall runoff. This could cause erosion, which is dangerous for bare soils. In the case of saturated soils and minimum slope, the water will be over the soil, in some cases as a lagoon, dam or reservoir.

It is observed that when rain falls on the surface part of it is always absorbed by the soil. However, the type of soil determines the absorption rate. If the rainfall intensity is high then after absorption the excess water introduces a phenomenon called surface runoff. Surface runoff is an essential part of the water cycle and it can be defined as the free flow of the excess water after the absorption. According to the soil physics water always move towards the low potential. That means surface runoff causes the excess water to flow towards low altitude and in this way river, sea or other natural water bodies get that water. The excess water can be stored by water surface and underground storage systems. The dams, intentionally dugged storage pools are common examples of such storage facilities. However, if the excess water flows horizontally for some time due to the geographical structure and cannot move due to some natural or artificial blockages (houses, rocks, holes) then it can cause the waterlogging.

When the rainfall takes place, the resulting water will either infiltrate into the soil or it will flow over the land surface and constitute rainfall runoff.
The amount of water that can infiltrate into the soil depends on a number of factors including, the intensity of rainfall, permeability of the soil surface, presence of vegetation, topography, etc. The infiltrated water may ultimately reach the groundwater. This water is generally harvested by using bore-wells.
The runoff takes place when the land has some slope. The water moves from an area of higher elevation to a region of lower elevation. If the land surface has no slope at all, the runoff will not take place and waterlogging will be the result. The surface runoff, ultimately, ends up in the surface water sources, such as rivers, ponds, lakes, swamps, etc.
Hope this helps.