On the website ethgasstation.info you see the current fees for fast, standard and safe low transactions, assuming that there are always more safe low transactions waiting to be mined than standard or fast transactions, and that there are always more transactions waiting than the capacity of the network, why are all safe low transactions mined eventually? Do miners give priority to those transactions that have more time waiting to be mined?
It's all based on best estimates. According to them that price "guarantees" that the transaction will be mined eventually (maybe in an hour or in a year?).
Miners don't have any incentive to include transactions which have been waiting for a long time. They want to maximize their rewards and therefore they just take whichever transaction gives them the highest gas price.
On the other hand some people submit transactions with gas price
0. Some clients even refuse to broadcast such transactions but they are totally valid transactions - they just may never get mined.
So, according to historical gas prices and near-future predictions Eth Gas Station calculates what is the lowest gas price which will most likely eventually be mined. In reality they cannot really guarantee that it will be mined - it's just the best estimate.