I was watching a movie and coming across with this sentence: "I'll be over right away" someone said on phone and hanged up.
I understand what is the overall meaning, but not be over
part of the sentence!?
One of the meanings of 'over' is 'to another place'. When people are going from one place to another, they can call that 'going over' to the other place. If someone says 'come over' they mean 'come to my house or apartment, or my current location'.
'I'll be over right away' means 'I will be where you are very soon; I am leaving now'.
One of the meanings of 'over':
Meaning of over in English
Over adverb
across; from one side or place to another:
Why don't you come over (= come to my house) for dinner on Thursday?
A friend of mine from France is over visiting us this week (= a friend came from France and is staying with us).
English commonly uses "over" that way to speak of a visit, e.g., "I will come over later." "We'll come over to your house tomorrow."
The word in that use is classed as an adverb.
See American Heritage Dictionary:
AHD "over" 3e
c. To one's place of residence or business: invited us over for cocktails.
The form "will be over" means the speaker will have arrived very soon.
Another word is used very similarly: "I will be by later."
"He came by yesterday."