Can someone explain this to me as I don't get what's written in this section of datasheet A piece code written in C showing the difference would be great too . thanks in advance.
Single conversion means, you trigger the conversion and it is done once. When the conversion is finished you have one result and the ADC is not doing anything more (not without a new conversion start trigger).
Free running mode means, the ADC is automatically starting a new conversion each time the last one finished. You don't have to retrigger the ADC in this mode.
I'm not sure what kind of code you want so see here, you can do all kinds of weird and wonderful stuff.