Assume you have a perfect system, not showing any error, and your sensor is totally linear. Further assume, that you have an error free 8bit ADC, with a resolution of 5V / 256 = 19.6078mV and your sensor gives you 19.6078mV per °C. Then, ADC reading is just your temperature. No additional calculation has to be done, no look-up table is needed.

But reality looks different! Each signal conditioning stage has it's own error in terms of offset, gain and unlinearity. Then you cannot easily determine result of temperature measurement.

Many different ways can help you to recover accuracy again.

1. Calibration using trimmers and other stuff being inserted in analog signal conditioning circuitry. This will only help to calibrate for offset and gain errors. Unlinearity normaly cannot be calibrated by such a scheme.
Cirucit recommended by me (the one using KTY 10-6) used this methode. Acceptable linearity and gain accuracy was assumed, and circuit needed only to be calibrated for offset error, caused by tolerance of R25 (resistance of KTY 10-6 at 25°C).

2. Today such calibrations are often done by using digital potis. These can be set by microcontroller himself running some self calibration routine.

3. If signal conditioning shows some intolerable unlinearity and some linearization has to be done, things become further complicated. One methode is to correct result of measurement by making a polynom approximation. This is often done with precision pressure transducers: You insert actual data of sensor reading and temperature into a n-th order polynom and result of calculation gives you the corrected data.
Coefficients of polynom are often given directly by manufacturer. But, only errors of transducer can be corrected by this methode. If rest of signal conditioning circuitry also shows some errors, they must be corrected by a different nethode.

4. If polynom approximation is too complicated, either because there don't exist coefficients of manufacturer or complex calculation would need too much time, then concept of look-up table is widely used. 8051 family was designed to ease the intense use of look-up tables.

Look-up tables are built by the help of a reference sensor NOT showing any relevant error. As Erik has explained, in such a look-up table can also stand only the deviation from correct data.

Kai