that happens as we age it's normal. it indicates a lower amount of body fat in your hands. it can also indicate muscle strength in the hands - the firmer your muscles are the more chance the veins have to stand out. so unless they are bulging really badly or turning into varicose veins (unlikely on the hand) or causing you pain there isn't a need for concern. in this case it's more a symptom of anxiety than anything.
i've noticed my veins in my hands are more prominent sometimes lately i'm a29 yr old female with no health problems. i have no health problems other than anxiety. it's really scaring me.