How does a Linear Feedback Shift Register (LFSR) generate pseudo-random sequences?

An LFSR is a shift register with feedback from XOR of selected taps to the input. With proper tap selection (primitive polynomial), an n-bit LFSR generates maximum-length sequence of 2^n - 1 unique states before repeating (excludes all-zeros). The sequence appears random statistically but is deterministic. Applications include: pseudo-random number generation, built-in self-test (BIST), CRC calculation, data scrambling, and spread-spectrum communications. Fibonacci and Galois LFSR configurations exist with identical sequences but different internal states.