1. Thorns are the sharp points on some plants and trees, for example on a rose bush.
2. Your sides are the parts of your body between your front and your back, from under your arms to your hips.
If you describe someone or something as a thorn in your side, you mean that they are a continuous problem to you or annoy you. • Money problems have been a thorn in our side since the day we got married. • Health inspectors are a thorn in the side of most restaurants.
This idiom is basically a metaphor. If you have a thorn in your side (or flesh), it will likely be a source of constant irritation. The expression appears in several books of the Bible; the Book of Judges refers to enemies who "shall be as thorns in your sides," and in the New Testament Paul refers to his infirmities as "given to me a thorn in the flesh".
In the cartoon, the thorn represents Chávez, whose foreign policy was often a source of headaches for the US, here symbolized by Uncle Sam. Not only did Chávez refer to ex-president George W Bush as the devil and a donkey, he also often rallied behind its enemies. Read Bob's own commentary here.
See The Cagle Post for more Chávez cartoons.