If one of the testiclel is having some visible vein on it, what does it mean?

Varicocoele. An enlarged blood vessel or varicose vein in the scrotum is called a varicocoele and is usually harmless unless it becomes inflamed and painful, at which time you should see a physician.
Varicocele. Rarely do varicoceles become symptomatic. More often they are left sided. They can cause a dull ache. They may cause testicular atrophy. They may be a cause for male infertility. Update me if you need more information.
Varicocele? Sounds like you may have a varicocele or dilation of veins supplying the testicle. More common on the left side, are generally described as "bag of worms". Varicoceles may cause pain, testis damage/atrophy (generally when they develop in younger males), and infertility. If the varicocele is resulting in one of these symptoms, treatment may be necessary.
Varicocele. This is probably a varicocle, or dilated veins. More commonly found on the l testicle. If asymptomatic or there are no fertility issues, then just exam on occasion. Follow up with a urologist if increasing discomfort or you have fertility issues.