My lover has just been diagnosed with second degree skin burns. I am worried but she acts like it is not a problem. Who can tell me what it means?

Can be serious. - 2nd degree goes thru epidermis and may cause blistering - can be serious if large surface area or if gets infected- requires careful wound management and dressing to prevent that. It may also hurt a lot.
Burns. The % of the body that is burned is more critical than the degree of burn alone. If you have a second degree burn that involves a small area of your body, you will need pain meds and wound care and later (perhaps) some sort of grafting, but you are likely to do ok and survive, however, burns that involve large areas of the body in the 40-50% can be life-threaening.