While telling someone that you're depressed can be helpful for many reasons, it should not be understated how important it is to assess the situation before making your move. For example, some questions you will want to consider are who you want to open up to, why you want to open up to them, and whether you feel that they will be receptive to the news. Unfortunately, the truth of the matter is that depression (along with other mental illnesses) still carries a very negative stigma in our society. While this may not always be the case, this is generally true for most situations, and you need to be very careful. You'll need to figure out if telling this person will be worth the risk. While we all wish that this were an ideal world where we could be open about mental illness, the world isn’t there yet.
In a professional work setting for example, declaring that you suffer from depression may open you up to discrimination. On the other hand, you may have a very understanding boss who will be accommodating if you ever need a day off, or need additional support on difficult days. It's up to you to assess the risk of opening up. Risks are also present with family and friends. You may have those who are completely dismissive, e.g. they don't believe mental illnesses are truly an "illness", or they may be on the other end of the spectrum and be incredibly supportive. Again, this risk is up to you to assess.
My opinion is that if there is a need for that person to know, if there is a good reason why you want this person to know, if there is a very good chance that they will be supportive, and if there is very low risk that they will react adversely to the news, then it may be a good idea for you to tell this person that you suffer from depression. Otherwise, you might want to hold back.
The insight I’m offering here comes from my own experiences, along with things I’ve learned and researched over the years. In my own experience, my parents weren’t receptive, and opening up to my school or workplaces would have had detrimental consequences. Some of my “friends” were not receptive, and we shortly went our separate ways. A few of them were very receptive, and were there for me during the darkest times.