What is a SMS Gray route?

Gray route

It is rather a subjective term, it almost exclusively relates to A2P SMS traffic (in theory a Grey route could also be used to send P2P traffic). Grey routes are a way of sending SMS via an operator where the the entity sending and/or their supplier do not have a commercial agreement or relationship with the receiving operator. In the more dubious cases there may actually be a contravention of the terms of use stated by said receiving operator (i.e. illegal - in the UK a civil offense).

For A2P traffic a good example of this would be sim boxes (modem farms). This is where A2P traffic is generated and sent over sims (installed in modems) intended for P2P uses. The advantage of this is that with enough sims installed, a large volume of traffic can be sent at relatively low prices, with little short-term fear of filtering or being blocked as the controlling operators believe the messages sent to be generated by a human being. Some load bearing between sims has to take place to ensure that a 'human being' is not sending an impossible amount of messages a day.

The more borderline definition of a 'Grey Route' might contain some SS7 routes. SS7 is the international signalling network used by operators to send each other their P2P traffic, there is usually some kind of 'net-off' agreement but in some cases operators could charge each other according to an AA19 agreement. The prices are usually low or none existent and so SMS Gateways who are connected to either an operator (other than the one they are sending to at the time) or SS7 can send their SMS traffic cheaply and in theory quite reliably. If the supplier has a direct connection to an operator or SS7 then the SS7 route cannot be said to be 'grey' but the more suppliers in the chain the more quality and latency issues there will be when sending, making the route less reliable and by some definitions, 'grey'. 
With more links in the chain and as there is no specific commercial arrangement between those sending and the operator receiving, the A2P traffic is liable to be detected by the operator at some stage and then the messages (and those like it) will be blocked. This is because bulk SMS A2P traffic is sent during short periods, in high volumes, with similar characteristics such as Sender ID and content - making it easily detectable by the operators and easy to filter.

Moral: If you are sending stable, legitimate traffic only, use suppliers who are either connected directly to operators in the country (or region) or who employ a 1-hop strategy via local partners who are directly connected to the operators.