You be regarded by native speakers as 'fluent' in English, even if you have an accent, and even if you make mistakes. Being considered fluent is very important because it gives people a greater sense of trust in the effectiveness of their communication.
'Rhythm' is one of the many different factors that contribute to fluency in English, and it is also one of the most important. 'Rhythm' refers to conversational ‘tunes’ of the language: the pitch of the voice rising and falling appropriately, and the volume of the voice going up and down, so as to achieve different shades of meaning. All languages have particular rhythms.
Why rhythm is important
Trying to learn a language without paying attention to its conversational rhythm is like trying to learn a song from the lyrics alone. You can't do it - it's not just the words you need to know, it's the music as well. Many overseas doctors overlook this aspect of language learning. They think that if they know the individual words, and if they understand the grammar, that it will all come together automatically.
But this is not the case. If you can use appropriate rhythms in your speech, you will find that more people will be able to understand you more easily.