English may be the language of the world now but it is spoken in so many different ways that I often hear people talking and I have no idea that they are speaking English. The reason: accent. Accents define who we are and for those who speak English as a second or third language, accents that they carry over from other languages (particularly from their mother tongue) can make it harder to follow. Our brains also work differently when we speak another language. Until you reach a level of fluency in a language that you can think in it, thinking in your native language and talking in another language produces rather funny situation. When I speak Japanese or Spanish, sometimes I mix up words and forget what language I am talking since both are foreign to me and I am often thinking in English.
So can you completely get rid of your accent?
Yes, with enough training, but unless you have to, don’t (you can take accent reduction courses). An accent is a great icebreaker and often attracts members of the opposite sex. What if others don’t understand you? Speak slowly and spell it out, if needed.