Your columns act as columns are supposed to do. You could insert a column
break in the start of the first column of page 2 to force your content to
move to column 2. However, if you want certain content to remain in the first
column and other content to remain in the second column, you could insert
your data in 2-column tables instead of ordinary columns.

If you create only a single table with 2 columns and 1 row and insert all
data in that table, the row can continue from page to page, still keeping
left- and right-column data separated. If the row stops at the bottom of the
first page even if you insert more data, select Table > Table Properties >
Row tab and turn on the “Allow row to break across pages” check button.

If you want the data on each page to be separate: create one table per page,
each with 2 columns and 1 row.

If you need information about working with tables, see the articles at:
http://www.word.mvps.org/FAQs/TblsFldsFms/TableBasics.htm

What are you trying to use: table columns or text columns?

If you are using text columns, something could be wrong with the
settings. You can try fixing it via Format | Columns: First, click the
"One" option, click OK. This should fix any corrupt settings for
column width. Then, go back to the dialog box and set the desired
option (number of columns, spacing, etc.).

To learn more about text columns vs table columns, see this article:

The strait and narrow: using columns
http://word.mvps.org/FAQs/Formatting/UsingColumns.htm