You have players 1, 2, 3 and 4. In the first round:
1 plays 4
2 plays 3
Let's say 4 and 3 lose. Now we have:
WINNERS' BRACKET
1 plays 2
LOSERS' BRACKET
3 plays 4
Let's say 3 beats 4. 4, having lost two matches (i.e. doubly eliminated), is OUT. Now 1 beats 2 in the winners' bracket. Now we have:
WINNERS' BRACKET
1
LOSERS' BRACKET
2 plays 3
Amazingly, 3 beats 2! Now 2, having lost two matches, is out. So finally we have:
1 plays 3
However, since 1 hasn't lost any matches, 3 must win twice in a row to take the tournament! 1 only has to win once. 1, being the master that he is, wins the first match and takes the tournament! That's how it goes down.