Allah (Subhānahu wa ta’āla) began this great sūrah (Suratul Mulk) with praise and glorification of Himself, and He is the most deserving to be praised and glorified.
The meaning of تبارك (tabāraka) is تعاظم. Allāh is the one who, when performing dhikr of him, blessings are obtained from (when done sincerely for Allāh and in accordance with the sunnah of the Messenger of Allah (sallallāhu alaihi wa salam)). He is the one who sends down blessings and He is the one who bestows blessings on whomsoever He wills.
This word ‘tabāraka’ does not apply except when speaking of Allāh, hence it is not allowed to say to someone “Oh so and so, tabārak upon us”, as some of the ignoramuses say.
However, as for saying to someone, you are “mubārak”, then there is no issue with it, because the meaning of “mubārak” is that Allāh (Subhānahu wa ta’āla) has blessed you and bestowed his blessings upon you.
Allāh (Subhānahu wa ta’āla) said:
وَجَعَلَنِي مُبَارَكًا أَيْنَ مَا كُنتُ
“And He has made me blessed wheresoever I be (Sūrah Maryam: 31)
كِتَابٌ أَنزَلْنَاهُ إِلَيْكَ مُبَارَكٌ
(This is) a Book (the Qur’ān) which We have sent down to you, full of blessings (Sūrah Sād: 29).
Therefore, Allāh is the one who bestows blessings and places blessings in whoever, wherever and whatsoever he wills. As for mankind, they can not bless themselves, indeed it is only Allāh who gives mankind blessings and makes them blessed.
Slightly Paraphrased from Shaykh Sālih al-Fawzān’s ‘Mā Tayassara wa Tahassala min Durūs al-Qurān fī Hizb al-Mufassal’ Vol.2 Page 6