That error indicates something is wrong with your system. Specifically your Microsoft Visual C++ installation.
Try running the installer from the BF4 installation folder as administrator and then restart your computer. The default location of this installer is here:
C:\Program Files (x86)\Origin Games\Battlefield 4\__Installer\vc\vc2012Update3\redist
[Edited to include these details - EABarry]
In redist, find both the x86 and x64 versions of VCredist.exe. Run and install both versions, and your game should now launch without error.