"The sky is blue" -> signed by Alice -> Bob vouched for Alice -> Cindy vouched for Bob -> Dom vouched for Cindy -> Dom is in my own list of vouches -> Therefore I can reliably trust Alice's report that the sky is blue.
(The reliability of this information will increase with multiple vouches throughout this tree.)
A consequence of this type of information structure may be that traditional authoritative sources of information will become irrelevant almost overnight, because reliable and auditable word of mouth will outweigh a professional reporter anyday.
Next after that is the same thing, but multi-directional. This is a much longer chain, but much more useful too. Example:
"There is a person who needs help at location X,Y" -> Signed by Alice -> "I'll reimburse and reward whoever helps the person at location X,Y" -> Signed by Bob -> "I helped the person at location X,Y by doing Z" -> Signed by Cindy -> "I observed this and it really happened" -> Signed by Alice -> "I gave Cindy a gold nugget weighing 0.1 oz" -> Signed by Bob -> "I received a gold nugget weighing 0.1 oz from Bob" -> Signed by Cindy "I witnessed this exchange" -> Signed by Dom
A logical consequence of this information structure is rapid slide into irrelevance of traditional commodity currencies and radical decentralization.