Connector name/where to buy
It looks like a standard type socket(or plug/receptacle) for a 2.54mm pitch header.
Names like Molex, Tyco (now might be TE I think), Harwin, 3M, Samtec make various types of these.
If you go to Mouser, Digikey, Farnell and type header into the search you will get lots of options.
Places like Sparkfun and Adafruit will almost certainly have some options also.
You will need crimp contacts and a crimp tool to fit the wires (also sold at the above places).