If you were attacking and wanted to cast Giant Growth/Predator Strike, you would need to do this before damage if you wanted the creature to deal +3 damage.
Technically, it doesn't matter whether you cast it on the Declare Attacks or Declare Blocks phase, as long as it's before Combat Damage phase. But, the active player has the first chance to cast spells, which will be explained later on. After that, the non-active player is given a chance to cast spells in response.
Ignoring any triggered abilities involving blocks, that rule simply states that the active player (the attacker) is given an oppotunity to cast spells before anything else happens. As in, he is given the first chance to cast Giant Growth on his own creature or activate some kind of ability like Sparksmith's shooting ability or whatever else he may see fit to do. These abilities are now put on the Stack (as in, they haven't finished resolving yet). Now he/she passes priority to the next player (defending player), who then is given the opportunity to respond to his spell/ability with his spells/abilities. Then passes priority back to the original player. This repeats until neither player has any spells or abilities to put on the stack.
Then all things on the stack resolve- last played things resolve first.
Example:
*It is your Combat Phase- You declared Grizzly Bears as attacking me.
*I declare Glory Seeker as Grizzly Bear's blocker.
-You have first priority- You cast Giant Growth targetting Grizzly Bears.
--Priority is passed to me- I cast Shock targetting Grizzly Bears.
---You have priority again- You have no spells to cast.
---You pass prority to me- I have no spells to cast.
(Last Played Spells/Abilities Resolve First)
--Shock resolves, dealing 2 damage to Grizzly Bears. Grizzly Bears is sent to the graveyard.
-Giant Growth tries to resolve. The target is invalid, the spell is countered.
(A common newbie mistake
-You cast Giant Growth on Bears. Pass priority.
--I pass priority.
--You pass priority.
-Giant Growth resolves. Grizzly Bears become 5/5.
*You pass priority
-I cast Shock. Pass.
--Pass.
-Shock resolves. 2 damage is dealt to Grizzly Bears.
*You pass priority.
-I cast Lightning Bolt. Pass.
--You pass.
-Lightning Bolt resolves, 5 damage is on Grizzly Bears and it dies.
See the difference? Because I responded to Growth, I was able to take down the bears with 1 Shock. If I allow Growth to resolve, I need to cast additional spells to deal with the creature.
Another example that did actually happen to me:
*I own 5 1/1 Saproling Tokens.
*It is my opponent's main phase (doesn't matter which one).
-Priority starts with him- He casts Pyroclasm.
--Priority is given to me now- I cast Echoing Courage on one of my Saproling Tokens.
---Priority is given to him now- He casts Shock on the Saproling I targetted with Echoing Courage.
----Priority is given to me again- I have no spells to cast.
----Priority is given to him again- He has no spells to cast.
---Shock was the last played spell, so it resolves first. My 1/1 token takes 2 damage. It dies and goes to the Graveyard.
--Echoing Courage tries to resolve. The target was invalid and the spell is countered.
-Pyroclasm resolves. 2 damage is dealt to the rest of the tokens and they die.
Priority and the Stack aren't easy things to learn for most people. It takes time to learn them, but when you understand them, the game is essentially made better. If anyone has questions about the stack, just PM me.
