How long a high-priority transaction takes to evaluate
When a transaction is published to the network, every node that hears about that transaction will check to see if it is a valid transaction according to the network's rules. If it is not valid, it will be discarded, but if it is valid it will be added to that node's mempool. Nodes will relay valid transactions to their peers in the network, but there is also no requirement for a transaction to be known to all nodes before it is included in a block. A miner can put their own valid, but otherwise not published transactions into a new block they have mined.

Similarly, when a node hears about a new block, it will check to see if the block is valid according to the network's rules. If it is, then the node will update it's blockchain record to reflect any state changes incurred by transactions in that block. 

With each subsequent block that builds off the block of interest, there is a higher degree of certainty that the transactions included in the block of interest will be permanently included in the blockchain record.