Nuclear bombs are indiscriminate, as are earthquakes. They affect everyone in their path rather than picking or choosing. When something is indiscriminate, it makes no fine distinctions.
A dog who eats everything could be said to have indiscriminate taste. If you walk into a store and buy the first pair of pants in your size, no matter what they look like, you are an indiscriminate shopper. Usually though, you'll hear the word used to describe violent acts or natural events because these things do not have a specific target. They affect all people without considering the differences in their lives.