Synthesis is the process of creating a new perspective by analyzing the similarities and differences among a group of other perspectives.
Typically, synthesis occurs in academic writing when you are bringing together multiple sources.
A visualization of synthesis
Pretend you are working with five sources for an essay, as represented by the five colored dots below.
Notice how there are no connections between the sources; the five sources are simply listed in some arbitrary order. What if you need to synethesize the sources, though? You can start synthesising by noting the similarities and differences between the sources and mapping them accordingly.
Perhaps you noticed that A (blue), B (yellow), and C (pink) make similar arguments, so they are grouped together. You also noticed that D (red) and B (yellow) share a similar methodology, so they are linked together. But perhaps D (red) does not make the same argument as B (yellow), A (blue), and C (pink). And E (green) is completely out there on his own! So you can now see that there are several possibilities for synthesizing these sources.
The gray ring around these sources represents the synthesized claims that you can make. For instance, you might claim, "While multiple scholars agree that X, there is no overall consensus on this issue." Or you may claim, "Conflicting methodologies among research creates gaps in the research on X."
When you do not synthesize your sources, your writing tends to read like a grocery list of ingredients rather than a fully cooked meal. Take a look at the two writing samples below. The first one organized by sources (i.e. not synthesized) and the second one organized by claims (i.e. synthesized). You do not need to read the full text; just notice the highlighted parts.