Why do more tornadoes happen late in the day?
There are two factors at work here:


Actual occurrence of tornadoes,
Reports of tornadoes.


Tornadoes are primarily associated with supercell thunderstorms, though they can also be associated with landfalling tropical cyclones, squall lines and bow echoes.  Thunderstorms are favored in the afternoon to early evening hours as this is when integrated solar heating throughout the day has warmed the boundary layer enough to kickstart convection (through reaching the convective temperature or eroding the capping inversion).  Because of this, supercells are going to tend to initiate in the mid to late afternoon and if they produce tornadoes it will be in the timeframe maximized in your graph.  

The tornado record is far from perfect and is based on verification of tornado damage.  That damage will only be surveyed if a potential tornado is reported or radar strongly suggested that one may have occurred.  A small tornado in the middle of nowhere from an unimpressive storm at night surely may exist, but a record of it may not.  This is also true of middle-of-nowhere tornadoes during the day, but those may have a slightly higher chance of being reported by a storm chaser.  No one smart chases at night.