来 (lái) and 去 (qù) are both words that help to express direction from the perspective of the speaker. 来 (lái) means "come" (towards the speaker), while 去 (qù) means "go" (away from the speaker). For example, if you are in China, a local person might ask you: "When did you come to China?" using 来 (lái). Another example is if you want to go from China to Japan, your friends might ask you: “When are you going to Japan?" using 去 (qù).
Seems really easy, right? Well, learn them well now, because you'll get a lot of mileage out of these words in future grammar patterns.
来 / 去 + Place
For the examples below, keep in mind that if the speaker uses 去 (qù), then she is not at the place mentioned now. If the speaker uses 来 (lái), she must already be at the place mentioned. Just stay consistent with this, and you're good.
来 (lái) and 去 (qù) can both be paired with other simple verbs to demonstrate the direction an action has taken. For example, 进来 (jìnlái, "come in"), 进去 (jìnqù, "go in"), 出来 (chūlái, "come out"), 出去 (chūqù, "go out"), 回来 (huílái, "come back"), 回去 (huíqù, "go back"), etc.
When you start tacking these two-character verbs onto the ends of other verbs, they are called direction complements, and are covered in detail in a more advanced article.