I did some testing and it seems to be the time of the start and ending points you provided. I chose a route which passes a time border (between Spain and Portugal) and this is what I get:
As you can see it takes into account the time zones, as the arrival time is actually before the departure time (because it's offset by the time difference).
Just to confirm, I looked up another trip by train this time and I chose a time 10:00 AM. I'm located in GMT+8, the train trip is in Switzerland, which is GMT+1. So if it is taking my computer's time into account, this would give try to find connections leaving at 3:00 AM. Of course, it wouldn't find any, as there are no trains running in the middle of the night.
As I get connections, this must mean that it is considering 10:00 AM in Switzerland and not where my computer is located.
I think with this (and of course also the official answermanual stated in the other answer) I think it's quite safe to say that Google gives you the local time at your departure and arrival points and does not take into account your system's local time.