Thanks to paulnamida's comment, this is a sub-genre of 異世界 (isekai, "different world") called 異世界転生 (isekai tensei, reincarnation on different world).
Nicopedia (Japanese) has an exclusive entry for this genre.
According to them, the definition is
元の世界の住人が死んで異世界で生まれ変わり、新しく人生をやり直すというもの。
Inhabitants of the original world die, reincarnated in a different world, and start a new life.
It has existed at least since 1988 in Japan with New Story of Aura Battler Dunbine, a 3-episode OVA of Aura Battler Dunbine.
古くから存在するジャンルで、日本のアニメでも80年代後半で既に近い特徴を持った『New Story of Aura Battler DUNBINE』が登場している [...]
In the genre that has existed for a long time, in the second half of the 1980s there was a Japanese anime New Story of Aura Battler Dunbine which has similar characteristics [...].
The cause of death can be anything, but a prominent one is caused by a truck, in which it's called "truck reincarnation".
転生なので異世界に行くには一度死ぬ必要があるが死因は様々で、トラックに轢かれて死ぬ、事件に巻き込まれて死ぬなど様々である。特にトラックに轢かれて転生する場合は「トラック転生」と呼ばれている。
Since it's necessary to die once to have transported into another world because it's a reincarnation, there are many causes of death, like running over by a truck, getting into an accident, etc. Especially, for reincarnation after running over by a truck, it's called "truck reincarnation".
Some prominent works in this genre:
- アルバート家の令嬢は没落をご所望です (The Daughter of the Albert House Wishes for Ruin)
- 異世界はスマートフォンとともに。 (In Another World With My Smartphone)
- 賢者の孫 (Kenja no Mago)
- 公爵令嬢の嗜み (Common Sense of a Duke’s Daughter)
- この素晴らしい世界に祝福を! (KonoSuba)
- 転生したら剣でした (I Was a Sword When I Reincarnated)
- 転生したらスライムだった件 (That Time I Got Reincarnated as a Slime)
- ナイツ&マジック (Knight's & Magic)
- 本好きの下剋上 〜司書になるためには手段を選んでいられません〜 (Ascendance of a Bookworm)
- 無職転生 ~異世界行ったら本気だす~ (Mushoku Tensei)
- 幼女戦記 (Saga of Tanya the Evil)
As for the reason why there are many works with this genre recently, Kevin fu's answer to a similar question would also apply here:
But the reason on why there's an influx of it being used is the fact that it currently sells when used in a light novel, manga, or anime title.