As a Cyndaquil, similar to Ash's Charizard, Infernape, and Tepig, Quilava was forced to deal with an abusive trainer before Ash caught it, although unlike Charizard and Infernape it did not actually belong to that trainer.
At first, Cyndaquil had difficulty using its Fire type moves but eventually mastered Flamethrower and was capable of using it with such power that Jasmine's Steelix was roasted within its own Sandstorm.
Cyndaquil was used frequently in the Johto region and was left at Professor Oaks lab when Ash went to Hoenn.
While training for the Sinnoh League, Ash brought Cyndaquil with many of his other Pokémon. However, Team Rocket tried to cause problems and Cyndaquil evolved into Quilava.
+ indicates this Pokémon used this move recently.* - indicates this Pokémon normally can't use this move.
Quilava is Ash's first non-flying type Pokémon to know Aerial Ace.
It took Cyndaquill the longest of all of Ash's Pokémon to evolve.
So far, Quilava is the only one of Ash's fire types that did not evolve in its introduction series so far.
Quilava's Blaze ability has never been mentioned in the anime but while it was battling Jasmine's Steelix as a Cyndaquil, it used a Flamethrower that was strong enough to turn Steelix Sandstorm into a tornado of fire, implying that it activated Blaze during this battle.
Cyndaquil had been hurt badly by Steelix's Iron Tail and Blaze gets activated when the Pokemon using it has taken a large amount of damage.
However it should be noted that special abilities did not exist when this episode was first shown.
Pryce's Piloswine is another Pokemon that appeared to use its ability before special abilities were invented because it seemed to use Snow Cloak when Ash battled against him. Coincidentally, Piloswine was battling Cyndaquil when it used the Blizzard attack that seemed to activate Snow Cloak (although in the games, Snow Cloak only works when it is hailing).
Quilava was Ash's only fire type pokemon that isn't abandoned by its original trainer