A pseudorandom number generator is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. The sequence is not truly random in that it is completely determined by a relatively small set of initial values, called the PRNG's state, which includes a truly random seed.
Where as A random number generator is an algorithm or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. In practice hardware random generators are used which generates the number based on a physical process rather then an algo.
Pseudorandom numbers are important in practice for their speed in number generation and their reproducibility.