1. Showing a consequence or result:
* The weather forecast predicts rain, hence we should bring umbrellas.
* She studied hard for the exam, hence she received a high score.
* The company was losing money, hence the decision to lay off employees.
2. Indicating a logical conclusion:
* He was late for work, hence he missed the important meeting.
* The evidence is clear, hence the defendant must be found guilty.
* The company's profits increased, hence the CEO received a bonus.
3. Expressing a reason or explanation:
* The road is closed, hence we must take an alternate route.
* The restaurant was crowded, hence we had to wait for a table.
* The party was cancelled, hence we decided to stay home.
Remember: "Hence" is a formal word, so it's best used in written English or in formal speeches.