As we workout our muscle get wear and tear. Then our body repairs or replaces the damaged muscle fibres though cellular processes. To form stronger muscles than before.
Veins are in or under our muscles and they get damaged with muscles during workout. Due to frequent wear and tear of muscles frequently they get above the muscle groups and closer to skin. I should add frequent wear and tear is required so if you are way weaker before you get more damage to fibres and viens remain in stressed position for longer forcing them to pop near the skin.
As our muscles grow bigger these veins grow to supply blood to larger muscle groups. Like in the case of the guy below
