It is often best to format documents so that the whole table appears on one page, but sometimes you have no choice and the table has to span multiple pages. In that case, you really need to repeat the headers at the top of each page. You could insert a copy of the header row at the top of each page, but if you change any formatting or positioning this will be in the wrong place. Word can do this for you automatically with a simple click of a button. There are screenshots below, but if you want to get to the answer quickly, just go to the Table Tools > Layout ribbon and click Repeat Header Rows with the top row of your table selected.
Here are some screenshots to show you what I mean. Here is the table breaking over two pages:
Select the header row and then on the Table Tools > Layout ribbon click Repeat Header Rows.
And now the table looks like this.