To “get the Unicorn” is a euphemism for a man getting an erection.
In this usage to “get the Unicorn” is synonymous with “getting the horn”.
“Getting the Unicorn” is also the reason you should never travel in tracksuit bottoms – the other day a hapless man wearing tracksuit pants with a mega unicorn was spotted in the departure lounge of an airport.
He was battling valiantly to get it under control, but failed miserably, much to the amusement of his fellow passengers.
“That girl gives me the unicorn, man!”.