Options() is your default constructor. Structs and classes are equivalent in the sense that they can have methods and constructors. What’s after : is the initialisation list for Options(). It tells you that in your default constructor for Options():
- num_particlesis initialised to- NUM_PARTICLES
- ule_lbpis initialised to- false
- infileinitialised to an empty string
- outfileinitialised to an empty string
Similar line of reasoning applies for State_. 
solved Functions in Structures ? C++