The NCBI talks about "Evolution beyond neo-Darwinism: a new conceptual framework." (source).
What is the difference between the Modern Synthesis and the Extended Synthesis?
The term Extended Synthesis has been invented very recently and the concept was defended in these two papers
I read each paper when it came out and haven't reread them since. Here is a short summary of what I remember.
Those who want to use term Extended Synthesis
In short, they are arguing new findings have extended our understanding of evolutionary biology so much so that we should rename our theory of evolution. The main findings they are talking about concern the field of evo-devo (merging Evolutionary biology and Developmental biology). The subjects that they consider having radically advanced our understanding of evolutionary biology include niche construction and inheritance of niche, developmental bias, plasticity, cultural evolution and epigenetics.
Those who do not want to use term Extended Synthesis
We have discussed both papers in groups in my department and in short, we pretty much all ended up saying that:
It is true that our understanding of evolutionary processes have advanced a lot since the time of Wright, Fisher, Muller, Kimura, and others. However...
I recommend reading the 2014 paper as 1) offer both point of views and 2) is pretty short.
I do not know your level of knowledge in evolutionary biology but it might be a pretty bad idea to start with complicated subjects such as evo-devo, niche construction, epigenetics, developmental bias, etc...