Many people believe this, and there is some truth in it, but much less than is often supposed. What is true is that children, whose brains are still growing, do learn languages and all kinds of new things much more quickly than adults. However, once you reach your teens you lose a lot of this advantage, and the difference between the ability to learn in a young adult and one of for example 50 isn't really so great. Also, older people often have another advantage - they know how to learn and are often more willing to sit down and study, or practise regularly, than younger people who often have too many other things going on or maybe don't want to make the effort.
In the end, in most people the memory gets less good, and this is where learning languages can become more difficult. But it shouldn't be a real problem until retirement age or later, and many older people do learn languages successfully.