range: (Python 2 and 3) Creates an entire list in memory at once, faster for repeated iteration but can consume significant memory with large sequences.
xrange: (Python 2 only) Generates numbers on demand, saving memory for big ranges but slower for multiple iterations and lacks list-like operations.
The range and xrange functions are used in Python 2 to create a sequence of numbers. The implementation, however is different. The range function returns all the numbers in a list. Thus it consumes memory and is not very efficient. xrange creates numbers on the fly, using a generator. This makes it much more memory-friendly. However, in Python 3 xrange is not available. Instead, range behaves like xrange: it generates numbers lazily.
In Python 2, range and xrange both produce sequences of numbers but do it differently. Range makes a list of all numbers in the given range and returns that, which for large ranges could consume a lot of memory. Xrange returns an xrange object that produces numbers one at a time as you iterate over it, thus saving memory. That is very important when dealing with large data sets. In Python 3, xrange is gone, and the range function has been improved to work like xrange. It creates numbers only when needed while keeping the same functions.