The general definition of assimilation is the process of two different things coming together to blend and, in some cases, create a new thing all together. However, that is a very simplistic understanding of the process itself as there are many different types of assimilation.
Types of Assimilation
The following are some examples of assimilation:
Color assimilation - This is perhaps one of the easiest models that demonstrates assimilation. If you mix a small amount of the color red with a large amount of blue, the red is assimilated into the larger mix. Though the red is absorbed, it changes the hue of blue so that it becomes something different and shifts in the spectrum of color.
Cultural assimilation - Cultural assimilation happens when two cultures or groups of people influence one another. Cultural customs, traditions, and religious practices can all be assimilated between two or more cultures. Often times, these groups live near one another. Influence may be derived from trade, invasion, and/or intermarrying between the groups.
Religious assimilation - A perfect example of religious assimilation is the assimilation of Pagan customs and ceremonies into Christianity. When Christianity became the predominate religion, they took Pagan holy days such as Yule and the Spring Equinox, or Ostara, and claimed them as Christmas and Easter. They adopted traditions such as the decorating of fir trees at Christmas and the use of symbols of fertility at Easter such as Easter eggs.
Another example of religious assimilation would be that of the Romans and Greeks. When Rome conquered Greece, they adopted their gods; Zeus, ruler of the gods, became Jupiter, Poseidon, god of the sea, became Neptune, Hades became Pluto, and the list goes on.
Linguistic assimilation - This type of assimilation often occurs when two neighboring groups of people or territories influence one anothers’ way of speaking.
For example, in the North East of America, there is a very distinctive, almost nasal, accent. Within that large group, there are smaller pockets of accents -- a Boston accent would be different from a Brooklyn accent, for instance -- however, both accents are easily identifiable as the larger whole of a “North-Eastern” accent. Linguistic assimilation also occurs in popular slang. Often, neighboring communities will have different slang words for the same things. If you move from one place to another, over time, you will quite often pick up on, and assimilate your own language with, the new slang or dialect.
Physiological assimilation - Physiological assimilation refers to the conversion of ingested nutrients into energy that fuels the body as a greater whole. For example, a starch molecule will be broken down into smaller carbohydrates, some of which will be used for fuel and others which can be modified to become part of the cell structure of the organism.
Statistical assimilation - Assimilation in a statistical capacity refers to the gathering data over time to in order obtain a clearer picture of that which is being studied. Data is assimilated and allows the person compiling the statistics a better understanding of how things work over all. A piece of data collected is assimilated into the model and becomes part of the mechanism by which all of the subsequent data is interpreted.
These examples of assimilation should give you a better idea of all of the different types of assimilation and how they occur.