There are two things to consider here:
1. The two-legged tie format
From the last 16 until the semi-finals, clubs play two matches against each other on a home-and-away basis with the same rules as the qualifying and play-off rounds applied. In the last 16, group winners play runners-up other than teams from their own pool or nation, while from the quarter-finals on the draw is free. (source: uefa.com)
This means that the two teams face eachother twice; once at home, and once away. There are several reasons use this format, among them the fact that it's more fair and that it's economically beneficial.
2. The away goal rule
Even though it didn't come into play in this particular example, the "away goal rule" is still very important, especially when considering the term "aggregate score". The aggregate score is the "total score" over the two games - and also the main way of determining the winner of the two-legged tie. In this case, the aggregate score was 5-5, as both teams had won with 3-2 at their respective home stadium.
When the aggregate score is a tie, one team can still be declared the winner - due to the away goal rule. Let us say that the 2nd game (in Sevilla) had ended 2-1 (instead of 3-2). The aggregate score would then have been 4-4, but Sevilla would have been declared the winner. This is because Sevilla scored 2 goals away, while Fenerbahce only scored one. Thus, the only way a game in the Champions League can go to extra time and penalties, is if both legs end the same way - as the game between Sevilla and Fenerbahce did.
For further reading, take a look at the Champions League regulations, and in particular articles 7-8.