For custom fields,how does "depend on field" work?

Been using custom fields for our event registrations and it works well. Now I have a much more complex event (a symposium). It runs for 8 days. The default is to attend for all 8 days or they can attend on a daily basis (1-8 days) at a higher rate (the break even is 5 days) . By default we assume they will attend all 8 days, but some can only make 2-3 days. We need to collect how many days they will attend, the start day and of course calculate the fee.

To give an idea of the interaction and complexity. We also having a lodging/tenting option which changes the base and daily fees.

I'm thinking of using "depends on field" as one way to control calculation of daily fees and enable capturing start date. How does it work and when I enable it the "depends on field options" shows up. What does it do? and how does it work?

I've attached an image of our current paper registration form. Any thoughts would be greatly appreciated.

Thanks
Carl