This is the first Trunks we ever see in Dragon Ball Z, and he is from a future alternate dimension, where the evil Android 17 and Android 18 are using the Earth as a playground, doing what they wish, due to being the strongest beings at the time. In this alternate future, Vegeta died in the fight against the Androids, along with all of the Z Fighters apart from Gohan, who is his first mentor and martial arts teacher. As a result Trunks did not know his father at all, as he was only an infant at the time, and so when he finally meets his father in the past, he is seen to be constantly trying to impress him.
Future Trunks travels back in time in order to warn Goku about the Android threat in the future, but upon arrival he is greeted by the Mecha-Frieza with his father King Cold. They had come to Earth in order to seek revenge upon Goku's loved ones. Trunks, then a young teenager, did not look like much of a threat to Frieza, and he freely told him so. Frieza was then given three oppurtunities to kill Trunks, but Trunks was able to block and dodge the attacks with ease. Trunks then performs what he calls his Burning Attack, which is followed up by his sword. Frieza was once again in more than one place at the same time. Had Trunks not shown up at that time the people of Earth would have surely been killed, because Goku was still on the way to Earth at this time.
When they train in the Hyperbolic Time Chamber together Trunks surpasses Vegeta in power, due to being a Halfbreed Saiyan. Throughout the year that was spent in the Time Chamber, Trunks realised Vegeta's real sense of Saiyan pride. With this knowledge in mind, Trunks hid his true power level to spare what pride Vegeta had left. Trunks had managed to reach what is called a Ultimate Super Saiyan, where the Saiyan is still Super Saiyan 1, but have trained a lot and are on their way to Super Saiyan 2. In this form, if they power up enough, their muscles will expand a lot and because of this their speed decreases.
Trunks is the first Saiyan to take on Perfect Cell with the intention of destroying him, although Trunks' power was enough to deal significant damage to Cell, Trunks was too bulky and slow, and this gave Cell the upper hand. Trunks quickly realised that he was too slow and gave up hope right before Cell's eyes. The battle hungry Bio Android, however, was entrigued at how strong Trunks had become in such a short period of time and posed a challege to the strongest fighters on Earth (Z Fighters, Vegeta and Android 16) to train as much as they could over a period of nine days. Then at the end of these nine days all the fighters of Earth must compete in the Cell Games. Trunks then left the battlefield and spread the word about the Cell Games, then when he reaches Kami Tower he declares a position in the "Hyperbolic Time Chamber" and trains for a whole year in one day.
When Trunks emerges from his training he is powerful enough to compete in the games and although he wouldn't be able to take on Cell alone, he is definitely strong enough to return to his time and destroy Android 17 and Android 18. With nothing to lose Trunks left with all the fighters of Earth to where Cell awaits. Trunks never gets the opportunity to kill Perfect Cell and during the fight between Gohan and the Bio Android, Trunks is impaled through the chest with a powerful energy blast and left for dead.
Trunks remains dead until he is revived by Dende's new Shen Long at Kami's Tower well after Perfect Cell is dead. After the celebrations Trunks says his goodbyes and returns to his time and dimension. After reuniting with his mother, Bulma, Trunks sees a News update on Android 17 and Android 18 and quickly powers up. Meanwhile the Androids are about to kill another innocent man, when all of a sudden Trunks hurtles a very accurate energy attack, narrowly missing Android 17. The cocky Androids foolishly underestimate Trunks and try to rush him. Trunks easily dodges all their attacks and punishes them duely, when he obliterates
Android 18 in a point blank energy blast. Android 17 looks on in disbelief and his feelings soon turn to hatred when the outpowered Android charges Trunks again, but he too is terminated with ease.
The completely unscathed Trunks returns to his home and everything seems at peace with the Earth except for one thing, Cell. The determined Bio Android in his weakest form, still roaming around for the now non-existent Androids, comes across Trunks and Bulma saying their goodbyes before the Time Machine. Trunks is about to leave when he senses Cell and sends Bulma away, Trunks then turns toward Cell and begins to taunt him with his knowledge from the alternate past. Trunks informs Cell that he has killed the Androids from the current time, and that the Androids of the alternate past have been destroyed as well, so all of his hopes for Perfection are crushed.
The weak and cocky Cell approaches the Halfbreed Saiyan under the false impression that he is as weak as Trunks was when he initially went back in time and warned Goku. The fight then begins and Cell is clearly outclassed as Trunks avoids Cell's every attack. Trunks then takes action by grabbing Cell's tail and swinging him around in a circle, building up momentum, and then hurtling him high into the air. Cell then realises that he has no hope against the new Trunks, and begins to prepare a Kamehameha Wave large enough to destroy the planet, knowing all too well that he could survive in space. Cell begins the formalities of the attack but is interrupted when Trunks unleashes all of his strength into a massive destructive wave of energy which incinerates Cell.Future Trunks