The are three core sections with many different toggles and sliders on the custom difficulty screen. The core sections are: General Options, Career Options & Advanced Options. For the sake of completeness I will explain what all the toggles in all the sections.
Allow Reverting Flights
This toggle allows you to revert a flight too one of two states, editor (vehicle assembly building or space plane hanger) or to launch. These choices can be accessed through the game menu (default key ESC) at any time during a flight.
This controls the ability to load quick-saves (note: Quicksaving can be done regardless of the state of this toggle, but you can only load a quick save if this is enabled). Quicksave/quickload can be done at any point in the flight using the relevant keys (defaults: F5 is quicksave, F9 is quickload)
Missing Crews Respawn
With this option enabled, Kerbals will respawn a short period of time after their death, and will be available for new flights.
Auto-Hire Crewmembers before Flights
This is a convenience feature. Without this option, if you try to launch a crewed vessel but have no crew available in the astronaut complex, the vessel will spawn but be uncontrollable (unless the craft also has a probe core) enabling this option will cause the game to auto hire enough crew to control the craft.
No Entry Purchase Required on Research
When you unlock a technology, all the parts associated with it have a "Entry Cost", like buying the blueprint, you can not use that part until you have paid the Funds for this "blueprint" (once you've paid this fee, you will still have to pay for manufacturing). Enabling "No Entry Purchase" disables this initial cost and all parts associated with that technology are unlocked as soon as you research that technology.
This option prevent the building of your space centre from being destroyed when hit by parts of your vessels. Destroyed buildings are unusable unless rebuilt, which costs a lot of Funds.
Allow Stock Craft
The game comes with some example craft, this option allows you to use these example craft in this save game.
These three sliders control your initial Funds, Science & Reputation.
This section controls the modifiers applied to contracts and this Science, Funds and Reputation they award. These sliders can be split into two sets of three sliders: Contract Completion Rewards & Contract Failure Penalties.
The Contract Completion Reward sliders control how big the rewards are for completing a contract, here higher percentages increase the amounts awarded. The Failure Penalties sliders control how much is deducted from you if you cancel a contract or fail to complete it within the allotted time, here bigger percentages increase the amount you lose.