Complete the task or action and then you will unlock the reward shown.

Akuji's prototype bike - Ronin mission 11.
Attack helicopter - Epilogue mission 4.
Bandit - Multiple driving stunts.
Brotherhood vehicles - Brotherhood Mission 11.
Buggy - One Chop Shop list.
Combine - Two Chop Shop lists.
Demolition derby vehicles - Demolition Derby level 6 in University.
Donnie's vehicle - Brotherhood mission 2.
Escort vehicles - Both Escort instances.
Gang customization cars - 15% hoods conquered.
Gang customization cars (even more) - 65% hoods conquered.
Gang customization cars (more) - 45% hoods conquered.
Julius' car - Bonus mission 1.
Maero's monster truck - Brotherhood mission 11.
Medical helicopter - Ronin mission 7.
News helicopter - Sons Of Samedi Mission 3.
Ronin vehicles - Ronin mission 11.
Saints ambulance - All Ambulance missions.
Saints fire truck - All Firefighter missions.
Septic truck - Both Septic Avenger instances.
Sons of Samedi vehicles - Sons of Samedi Mission 11.
Super Taxi - All taxi missions.
The General's Bulldog (Hummer with unlimited chaingun ammo) - Sons of Samedi Mission 11.
Tornado attack helicopter - Final mission of the Ultor epilogue.
Ultor APC - Epilogue mission 2.