Imagine you paired everyone in round #1 of a 6 player bracket: 1v6, 2v5, 3v4. Three players would advance, leaving you with a bad situation. See top portion of the image below.
To avoid this, byes should be awarded in round #1 to two players. Following this rule, round #1 (sometimes referred to as the qualifying round in this scenario) would have 3v6 and 4v5. The two winners, or qualifiers, would advance to join players 1 and 2 in the next round. The bracket at this point becomes balanced with 4 participants, a power of 2. See bottom portion of the image below.