What is embedded programming? What are the basic skills required to learn it?

Embedded Programming basically means programming an Embedded system. Assuming you know what an Embedded systems (a simple google search would suffice), programming an Embedded system basically boils down to programming the processor of the Embedded system. In most of the cases, it is just a micro-controller. In some cases where the complexity and processing power required is high, it is an high-end processor with an operating system.

Coming to the second part of the question, few years back, microcontrollers could be programmed with mostly C or C++ (I think there’s some hardware support with python now as well). So basically you need to be well versed in C or C++.