Back from the Brink is an enchantment from Innistrad that allows you to reuse creature cards that are in your graveyard. Whenever you could normally cast a sorcery, you can exile a creature card in your graveyard and pay the mana cost of that card to put a token copy of the exiled card onto the battlefield under your control.
It is important to note that this is not casting these cards. You are activating an activated ability that puts token copies of these cards onto the battlefield. Because of this distinction, there are a few things to keep in mind. One thing to know is that these are not creature spells, so they cannot be countered by spells and abilities that counter creature spells.
Another thing to remember is that because you are not casting these cards, effects that change what you pay for creature spells will not apply. The effect of Heartless Summoning that lowers the cost to cast creature spells will not be applied. Similarly, the additional cost of Makeshift Mauler that requires you to exile a creature card in your graveyard will not have to be paid. This is because that cost is only paid when you cast that creature spell.
Effects that change when you can cast creature spells do not matter. In other words, the flash ability of an Ambush Viper card in your graveyard will not allow you to use Back from the Brink’s ability when you can cast instants. The timing restriction on the activated ability will still determine when you can activate the ability.
Finally, it is important to note that the creatures that are put onto the battlefield with this ability are both complete copies and tokens. Because they are copies, abilities of these creatures that are applied as they enter the battlefield and those that trigger when they enter the battlefield will happen. A token copy of Festerhide Boar will get two +1/+1 counters if a creature has died earlier in the turn and a token Fiend Hunter will exile a targeted creature.
Also remember that copies have the mana cost of the original card, even though they’re tokens. Activating Ratchet Bomb with zero counters on it will not destroy the token copies of that Festerhide Boar or that Fiend Hunter.