What does it mean if the veins in my sack connected to my testicles get bigger? (serious question)

Varicocele. Sounds like you 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.
Possible varicocele. Varicoceles usually develop on the left side and feel like a "bag of worms" if you feel them when standing. Just make sure there is no lump on your testicle. Check with a urologist if this is bothering you. Varicoceles are by and large harmless but can be associated with male infertility.