The concept of trustnet is that with sharding, we will eventually reach a network where no one node has all of the chain data. However, in order to mine a block on a shard, it may need to import blocks from other shards. Including incorrect blocks will result in the new mined block being invalid so a miner must completely trust the source of data about validity of other shards.
The solution is the trustnet. The most basic use is a mining pool operator will run their nodes with the same trustnet keys so that they trust each other for other shard validation and can safely import blocks from those chains.
For clients, a client may be configured to prefer to use nodes of a specified trustnet in order use trusted nodes that are giving correct information and not acting as address honeypots.