This might be something that's known generally but I just came by this today.

How it happened; My son asked me if I have been surfing with his Nexus 7 lately, as it was suggesting words on google search window that I did actually search for earlier this morning.

However, I had been using my laptop to do that, not the tablet !!

Speculation; as both devices are in the same WLAN, which is NATted to outside world, google is storing my IP address and as a shortcut showing the previous queries to any host accessing google afterwards using he same apparent IP address

Now this is really bad behaviour, as there is no guarantee that a particular IP address belongs to any given device after some time has passed, it might well be given to somebody on completely different town, even different country.