The cy.clock() is about controlling the perceived date of the app.
From the examples,
Let the test run as at a certain date
const now = new Date(2017, 3, 14).getTime() // April 14, 2017 timestamp
cy.clock(now)
cy.visit('/index.html')
cy.get('#date').contains('2017-04-14')
Typing into a field with a certain format
If you want to .type() a particular date string, convert with .toLocaleDateString()
const d = new Date() // current date
// or
const d = new Date(2017, 3, 14) // specific date
cy.get('input').type(d.toLocaleDateString('en-GB')) // type in as 'dd/mm/yyyy'
Combining the two, e.g testing validation
// Set clock to a specific date
const now = new Date(2017, 3, 14).getTime() // April 14, 2017 timestamp
cy.clock(now)
cy.visit('/index.html')
// Type in an earlier date
const d = new Date(2017, 3, 13)
cy.get('input').type(d.toLocaleDateString('en-GB'))
.blur() // fire validation
.should('contain', 'Error: Date entered must be a future date')