Translation:This scientific article may explain everything.
The verb 'açıklayabilir' has the suffix '-bilir' which means 'may/might/can'. So just as 'It explains'='Açıklar', 'It is explaining'='Açıklıyor', 'It may explain' translates as 'Açıklayabilir'. For instance if you wanted to say 'I can explain', it would be 'Açıklayabilirim'. 'You can explain'='Açıklayabilirsin'.
I was wondering how Turkish distinguishes here between 'may' and 'can'. In the context of this sentence, in english, the meaning is different. If it 'may' explain eveything you could get to the end of the article and discover that it doesn't. So it hasn't helped. If it 'can' explain everything then you are telling someone that they WILL definitely understand at the end.
Good question. I don't have the answer, but this reminds me how "Sen iyi bir öğrenci olmalısın" was said earlier in the course to carry BOTH meanings of "You must be a good student" in English. That is: both 1. You'd better be a good student (it's obligatory) AND 2. (judging from something you said or did) you must be a good student.