When you read you hear the sounds of the words in your head. When you write you say the words internally. When you listen you are matching the sounds you hear with the sound you know. And of course when you speak you are choosing sounds to convey your meaning. Even when you think in English you need all the sounds!
Pronunciation is important when you memorise new vocabulary. Learning the sounds, the stress and the number of syllables gives another hook for your memory.
Spelling and pronunciation are connected - even in English! You can help your pronunciation by observing spelling closely, and help your spelling by developing your pronunciation.
If your pronunciation is quite good you will be able to communicate more comfortably. If you speak to someone whose English is not so good you will be flexible enough to understand their meaning, and even to adjust your pronunciation to help them. It also saves time in communication because you do not have to stop and repeat and re-phrase.
When listening to rapid speakers you will be better able to pick out the key parts of their message. When expressing yourself you can worry less about being understood and think more about enjoying your communication.
Clear pronunciation helps you focus on the meaning of the message rather than the words and also helps you decide whether you are hearing new words that you may need to learn, or words you already know but did not recognise.
You do not have to sound like the British or American speakers on this app. There are many other accents used by native and non-native English speakers in the world. However your pronunciation needs to be understood comfortably by your listeners. And when you listen you need to understand English spoken in a range of other accents.