A look up table (LUT) is simply a matrix (mainly stored in a memory) which holds same values of complex functions (e.g. sine table). It is used to avoid complex calculation of these values where this would be too onerous for hardware or processor speed. In this way these values are simply addressed in some way and the calculation costs "only" one or more access in memory.
Hope this will be useful for you.
Mowgli
As an example of look-up table; in GSM you have each point of the shape of the burst stored in memory. This shape should be very well defined because it will influence the performance in TX mode. So the system before each burst transmission, just have to call this numbers from the memory (look-up table).
Regards
Lookup tables are particular implementation related to generic data structures . Let say tree's or linked lists . Some program do not require using data structures , but for complex programs dealing with referenced data carefull data structure selection and design is preferred . This will define code quality and performance .