A PRNG is a mathematical algorithm that produces a stream of numbers which pass statistical tests for randomness. Almost every online slot uses one rather than a hardware source such as electrical noise.
"Pseudo" means the sequence is generated by a formula from a starting value, the seed. In principle, anyone who knew the algorithm, the seed and the exact moment of every draw could predict it. In practice, gambling PRNGs are seeded from unpredictable sources, cycle continuously at high speed, and are kept secure, so the numbers cannot be predicted or influenced by players.
Approved test houses check that the PRNG's output is statistically random, that it is properly seeded, and that the way numbers are scaled to game outcomes introduces no bias. That testing is part of a game's certification for the British market.
For players, the practical upshot is the same as for any RNG: every spin is independent, and no pattern or timing changes the odds.