It's a pun humorous way to tell that you are still young!
I myself have used it a couple of times.
This simply means that the person is still energetic at that age and feels or appears 'young' .
Imagine a conversation: "
He is 45 years old.
"
"Old?
Look at his energy; he's 45 years young!"
Note that here, old does not mean having wrinkles or being on the verge of contracting diseases associated with senility !
The word old here means of a particular age , so don't connect old with aged person (बुज़ुर्ग) when it is accompanied by a number .
ell.stackexchange.com/users/3187/Maulik V
Years young 1 : describing how old one is in a humorous manner Example: I will be fifty years young next year.
Avoid using it if you are serious.
We're all getting older, so it would seem to make more sense to use "years old."
Exception: Benjamin Button 2
^
He would always say "years younger" 1.
dictionary.reference.com 2.
Wikipedia
ell.stackexchange.com/users/20213/Usernew
This is an illustration of markedness : a cognitive / linguistic phenomenon that is common to many languages, not just English.
Some adjective pairs are naturally asymmetrical:
Young / old Short / tall Dumb / smart
You would normally ask how tall a person is.
On the other hand, if you ask "How short are you?", then it feels unusual, and it's no longer a neutral question:
it's implying that you think the person is unusually short.
Similarly, if you ask "How young are you?", then it implies that you think someone is unexpectedly young.
If you say that "He is 80 years young", there is meta-information that the speaker thinks that the subject looks or acts younger than 80 years.
ell.stackexchange.com/users/5289/200_success
It is a form of flattery.
Instead of saying that the guy is old and infirm, the flatterer endeavors to imply that the flatteree is super-young for his age, sprite, full of energy, active, etc.
ell.stackexchange.com/users/27173/Ricky
The word "old" essentially has two meanings.
One is simply a measure of age: How old are you?
I am 5 years old.
In relative terms, a 5-year-old is considered young whereas an 80-year-old person is much nearer the end of his life
and we would speak of him as being "old" in the sense of being elderly.
The word has a lot of negative connotations and even teenagers refer to their 40-something parents as "old" in a dismissive, disrespectful way.
Using the expression "80 years young" is a way of flipping that around and suggesting that he is still very much vibrant and alive, the opposite of all the dreaded attachments of being "old".
ell.stackexchange.com/users/8026/shawnt00
Used in a humorous sense.
The speaker is trying to make light of age, which can sometimes be a difficult subject to approach.
It is used to make an older person feel more at ease with his/her age.
ell.stackexchange.com/users/27590/Amanda
My 74 year dad used to call himself as "74 years young".
He was full of curiosity and energy at 74.
So, it is okay to bend the rules of grammar and logic a bit, so long as the meaning comes through.
On the other hand, I would hesitate to say he is 80 years young for a stranger, in case the stranger feels I am not acknowledging or respecting his seniority.
ell.stackexchange.com/users/27582/RajuK
I've seen statements like "He is 80 years young" in many places. Also, I know that it means the same as   He is 80 years old.   Now, why do people use  'young'  instead of  'old'  if it means the same? Or am I entirely misinformed and the statement is actually invalid?
"He is 80 years young"
ell.stackexchange.com
<word-choice><phrase-usage>
ell.stackexchange.com/questions/75576
ell.stackexchange.com/users/27122/Varun Nair
Using the expression "80 years young" is a way of flipping that around and suggesting that he is still very much vibrant and alive, despite all the dreaded attachments of being "old". This can be a form of flattery. It is also a way of  describing how old one is in a humorous manner, as in "I will be fifty years young next year." This is a form of flattery and can be meant humourously.
This is a form of flattery. It can be meant humorously.