"I am sorry."

Translation: Bocsánat.

[JovaDuolinguo]

"Sajnàlom", what does it mean exactly?

[jsiehler]

Sajnálom is another way to say I'm sorry. If you take it literally, the meaning is close to "I regret it" (referring to a bad thing that happened), and you can use it to express sympathy for something as well as apologizing for something you've done. Elnézést is strictly an apology - closer to "pardon me" or "excuse me" than it is to "I'm sorry." (If you want to break it down to a literal meaning, it's like "[I ask your] looking-away," although I don't think anybody really hears it like that.)

[vvsey]

You can also feel sorry for somebody, saying "Sajnálom őt".
And "Elnézést" could be compared to someone "looking past" some mistake. "I am willing to look past this mistake" - "Hajlandó vagyok elnézni ezt a hibát". But in general usage "Elnézést" is just "Excuse me".

[louis743446]

I have never heard this statement in conversation. Bocsanot, bocsi, elnezest...are all common

[RobertJack948690]

Ditto

[deactivated user]

I put 'Én vagyok elnézést.' and it marked it as incorrect. :(

[bbigblue]

That is incorrect indeed. Mirror translation does not work here.
I can ask for forgiveness (Elnézést kérek.) or I can express that I feel sorry (Sajnálom.). Also see jsiehler's and vvsey's comment above.