Puff pastry, also known as mille feuilles (which translates to 'a thousand leaves'), is a classic French pastry belonging to the laminated (roll-and-fold) pastry family along with leavened puff pastry (also known as croissant dough), flaky pastry and rough puff pastry. The characteristic 'lamination' of alternate layers of butter and pastry dough (as you can see here in this raw pastry) is what gives puff pastry its many light, crisp layers when baked and it is the consistency of both these elements that will help determine how even these layers will form and how successful your pastry will be. The butter needs to be firm but pliable and a similar consistency to the dough. It shouldn’t look oily or be too soft and you should always be able to feel a little 'chill' in it while still being able to roll it out without too much pressure.
It does take practise to recognise, by feel, what the 'right' consistency is for your butter, but if you use the dough to compare it to, you will soon be well on your way to a successful pastry.