The Snake and apple image is maybe the most recognizable religious symbol there is.

It represents the first sin.
They lived in paradise in total innocence until the serpent (the devil) enticed them to eat the forbidden fruit from the tree of knowledge. alimentarium
In tattoos , the snake and apple design is not very common, it can represent the rebellious side of the wearer , and not being afraid of breaking social “norms”.

Other meanings behind snake and apple tattoos
Forbidden knowledge

The snake itself can represent hidden knowledge and the red apple being the ultimate temptation symbol, the two combined can represent the willingness to acquire not so common knowledge, not caring about consequences.
Betrayal

Again, a religious symbol being the betrayal symbol. the snake basically represents the devil , and the apple represents knowledge, both combined symbolize the willingness to commit a sin.
Greed

The snake can represent greed, temptation and greed in general. It’s self description is “an ugly creature that craves everything” (which includes money, sex and power). The serpent can also be used to depict narkiness (snakes are bad-tempered creatures), or deceitfulness.
The apple can represent greed in general or knowledge (as mentioned earlier).
Certain snakes are known to be venomous, but the apple represents the forbidden fruit, and forbidden knowledge is often not a good thing. So the snake and apple tattoo can be used depict a bad temper, deceitfulness or greed. Or it may just depict a rebellious character in accordance with what was discussed earlier.
Freedom-Fighters

The snake can represent freedom , while the apple represents sin or temptation (the forbidden fruit). Together they can be used to represent freedom fighters, rebels or those who are ready to go against the odds in the fight for a better world.
Freedom of speech

The snake and apple can be used as a representation for freedom of speech and freedom of thought. They may also represent self-expression and overcoming fears.This way the design is not so political, but still carries a lot of meanings towards personal life. On an abstract level it could symbolize individuality and independence.
Vampires (fantasy)

A snake with an apple in its mouth, engraved on the back of people; May represent an ability or state of being that is vampiric or alluring
The symbols, when deconstructed , can be used to mean many things. The apple represents temptation while the snake can signify a narkiness or bad temper on the part of the wearer.