This post will be short and sweet. You'll hear people frequently refer to "the Diaspora." In short, that's everywhere but Israel.
Being in the Diaspora or not can affect holiday observances. Some holidays that are two days in the Diaspora are only one day in Israel because that's how it's supposed to be observed. This is because the new month used to be announced by bonfires, and sometimes there was doubt as to which day a holiday would fall on. Therefore, the outlying communities observed the holiday on both possible days it could be. This halachic issue gets more complicated when a person living in the Diaspora visits Israel during an affected holiday or an Israeli Jew visits the Diaspora during an affected holiday. Generally, your rabbi will advise you to observe the holiday as you would where you live. When Israeli Jews visit the Diaspora, they're supposed to be careful not to be too obvious that they're observing only one day because it could confuse a Diaspora Jew into thinking that the day isn't actually a holiday with the yontif restrictions.
The Diaspora also goes to the idea of exile. The Jews remain in exile today, and the Diaspora is that exile.
Last but not least... For most readers of this blog, the Diaspora comes up in Israeli politics, particularly conversion politics. You'll often see news articles about the Israeli Rabbinate's policies affecting "Diaspora conversions." Because many converts want to make aliyah (or their children might want to), the Israeli Rabbinate's conversion policies/recognition necessarily affect how conversions are done abroad. Even if you personally don't plan to make aliyah (and you may change your mind), you should know how your conversion interacts with aliyah and the Rabbinate.