The core may be made by a twisted core ropes consisting of nylon yarn twisted into cordlets, which are then twisted into strands running the length of the rope. Each strand will contain 3 cordlets - the number of strands in the core depends on the diameter of the rope. Strands have a 'lay' depending on whether the cordlets are twisted clockwise or anticlock-wise. A core will contain a combination of each type to reduce chinking and twisting of the rope. A rope's flexibility affects how easy it is to handle and how easy it is to tie in knots.
Some climbers prefer more flexible ropes, because they're easier to tie.
But when loaded, those knots can become difficult to untie. Others prefer stiffer ropes because they're easier to thread through different climbing gear pieces and because knots tied in them are easier to get out. Flexibility is largely a matter of personal preference. Keep your rope clean. Dirt particles are extremely abrasive to ropes.