Entropy is a measure of how many different (microscopic) states would meet a given (macroscopic) description. For example, suppose we have 64 pennies on a chessboard. There's exactly one way for them to meet the description "all on square a1": the first penny would have to be on a1, and so would the second penny, and so would the third penny, and so on. On the other hand, there are 64!≈10^(89) ways for them to meet the description "one penny per square": there are 64 different pennies that could be on square a1, and after that's chosen there are 63 different pennies that could be on square a2, and after that's chosen there are 62 different pennies that could be on square a3, and so on. So "one penny per square" is much higher-entropy than "all on square a1". Similarly, a universe where all the matter/energy is in one place ("Big Bang") is lower-entropy than a universe where the matter/energy is all spread out evenly ("heat death").

There's a weird sort-of-law of physics that says "the entropy of the universe always increases over time". It is, in fact, the only known difference between the future and the past: all other laws of physics work the same in reverse as they do when running forward.