Added Benefit. In addition, consider giving characters who have both a relevant skill and a relevant tool proficiency an added benefit on a successful check. This benefit might be in the form of more detailed information or could simulate the effect of a different sort of successful check. For example, a character proficient with mason’s tools makes a successful Wisdom (Perception) check to find a secret door in a stone wall. Not only does the character notice the door’s presence, but you decide that the tool proficiency entitles the character to an automatic success on an Intelligence (Investigation) check to determine how to open the door.
This is what they mean. It is earlier in the chapter. When you use Investigation and / or Perception on a trap, the DM should give you more information about the trap. That may negate a roll that would otherwise be required.
Example: Bob has proficiency in Thieves Tools and Perception. He is scouting for the party and is actively searching for traps as he goes. The DM asks him to roll a perception roll and he gets a 22. The DC to spot the trap was 18. The DM will tell him there is a trap - and because he his proficiency with the tools necessary to disarm the trap, Bob will also be given a bit more information about the trap automatically, perhaps negating the need to roll an investigation to understand how it works.
Perception allows you to notice something others might miss. However, it doesn't explain anything to you.
Investigation allows you to utilize your wits to figure out how something works. However, you need to have observed something in order to figure it out, generally.
Thieves Tools allow you to put your knowledge to use and solve the problem.
A Pit Trap may not require an Investigation roll - once you see it, it is obvious what it is. However, if you do not spot it with perception, you'll fall in. Thieves tools (or other skills/tool proficiencies) may allow you to secure the trap so that it can be walked across, depending upon the nature of the pit trap.
A poison gas trap on a locked chest is a different beast. You need to spot the mechanism with perception, investigate it to figure out how it works, and then use thieves tools to disarm it (or, alternatively, just set it off remotely, etc...).
The way that I handle all of this, since the start of 5E, has been: When rolling a series of skill checks, greater success on an earlier check will make it easier for the PC to succeed on a later step. For example, If Bob rolls a really good perception check for finding a poison gas trap on a chest, I might lower the DC to figure out how it works - and if the roll is good enough, that could be an automatic success (if their 'passive' investigation would then beat the DC, for example).