I just started watching The Flash series, currently in season 2. So, Cisco gained his power when season 1 is nearly coming to an end. He somehow also affected by the particle accelerator explosion, and why he doesn't know he has power until several years later? What has triggered his meta-human power?
It wasn't several years, Not even 2. The particle accelerator accident happened on December 11 2013, while the season 1 ender happened in May 19 2015. Many metas had delayed power emergence as well.
What triggered Cisco's powers was being killed by Eobard, on March 24, two months earlier. But he didn't die, because Barry was up to his usual time travel stupidity (Season 1 Episode 15, Out of Time) and undid that timeline. This causes Cisco to start having nightmares. These nightmares are Vibe's basic powers to see across space/time/dimensions.
It's touched on 5 episodes later, in Season 1 Episode 20, The Trap:
His lucid dreaming is another part of his power. This is mid April 2015, a year and a half post-exposure.
Cisco didn't show more power earlier because of the trauma of the event and his fears of what his powers may do caused him to repress them.