Does an instruction like this: MOV P1.0, #1 makes the port P1 bit 0 High so i can drive an LED for example, or it just makes it FLOAT so i can use an external circuitry to light the LED. If so, does this mean that we can't output a "real" HIGH to the ports?
The 8051 (original 'flavors') does not output a '1' with much drive capability. It is better to connect your LED + resistor from the output to Vdd and drive the pin low to turn the LED on. You could also add a pull-up to Vdd and shunt the LED, but that wastes power.
Edit: as per request, below is the i8051 I/O structure from the MCS-51 manual.
The strength of the pull-ups varies according to the type, but can be as high as 30mA nominal for the brief strong pull-up, and tens or hundreds of uA for the weak.
It depends in the output pin driver.
If it is an Open-Drain type then the pin can either float or tied to ground.
If it is a Push-Pull then it is either tied to VCC or ground.
At many microcontrollers this can be configured so you should cehck the datasheet about the default setup.