Lo siento is the usual way of saying sorry in Spanish. It is used to apologize to someone when you have made a mistake. If you want to ask for permission you should not use 'Lo siento'. Instead, you should say 'Disculpe'. Both are similar, but slightly different.
How do you say 'Lo siento' in Spanish?
'I'm sorry' in Spanish is 'Lo siento'. You should use it when you have made a mistake and want to apologize. In English you can use 'sorry' if you want to interrupt someone. Or if you want to pass between two people who are talking. In these cases, you don't have to say 'Lo siento' in Spanish (before your interruption or passing in between).
These two words are only used to apologize. If you want to ask permission to do something in Spanish you should use 'Disculpe' (more formal) or 'Disculpa' (colloquial). 'Sorry' and 'Disculpa' are correct if you want to apologize. But to ask for permission you can use 'Disculpa' or 'Disculpe' only.
Emphasize your 'I'm sorry'
In English, if you want to emphasize your sorry you say 'I'm so sorry'. If you want to do the same in Spanish you have to say: 'Lo siento mucho'. In this language you put 'mucho' at the end of the sentence, to say that you are very sorry for something.
Where does 'Lo siento' come from?
Lo siento' comes from the verb 'to feel'. In English you use 'feel' as a presentation of your feelings. "I feel happy." In Spanish would be "Me siento feliz". It's a way of expressing how you feel. And, if you feel really bad about something you have done and you want to apologize, you will say, 'I'm sorry'.