What spells would be associated with my Draconic Bloodline sorcerer's Dragon Ancestor, for the purpose of the 6th-level Elemental Affinity feature?
I picked Brass Dragon as my ancestry; would it be fire spells?
The Draconic Bloodline sorcerer's Dragon Ancestor feature tells you to pick a type of dragon to serve as your dragon ancestor, with a table associating each dragon type with a particular damage type:
At 1st level, you choose one type of dragon as your ancestor. The damage type associated with each dragon is used by features you gain later. (SRD, p. 44)
The Draconic Ancestry for Brass points to fire. (SRD, p. 45)
The subclass then grants the Elemental Affinity feature at 6th level, which boosts damage for spells of that damage type (and lets you spend a sorcery point to gain resistance to that damage type for an hour):
Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, you can add your Charisma modifier to one damage roll of that spell. At the same time, you can spend 1 sorcery point to gain resistance to that damage type for 1 hour.
You add your Charisma modifier to one damage roll for a fire spell.
So is it just one spell a day? I get to apply that to?or with every long rest?
No limit. It is on each fire spell that you cast.
Example: if you cast the cantrip fire bolt ten times during a few combats, on each casting you get the bonus.
Elemental Affinity states:
Starting at 6th level, when you Cast a Spell that deals damage of the type associated with your Draconic ancestry, you can add your Charisma modifier to one damage roll of that spell. At the same time, you can spend 1 sorcery point to gain Resistance to that damage type for 1 hour. roll20 Compendium
Draconic Ancestry gives:
White Cold roll20 Compendium
Thus, a Brass Dragon Ancestry would give bonus damage to any spell that does fire damage when Elemental Affinity is gained at 6th level.
Specifically, draconic bloodline indicates that spells that do fire damage are "fire spells".