I cited this Islamic site earlier
"Initial, disjoined letters introduce 29 chapters of the Qur'ân. Different chapters begin with different letters: Alîf Lâm Mîm... Kâf Hâ Yâ... `Ayn Sâd... Tâ Sîn Mîm... among other combinations. People often wonder about their meaning. In truth, we cannot ascribe any particular meaning to these letters. Any particular meaning that these letters might have is known only to Allah. Ibn Kathîr, in his Tafsîr, informs us that Abu Bakr, `Umar, `Uthman, `Ali and Ibn Mas`ud all said that "the disjoined letters in the beginning of some chapters are among those things about which Allah has reserved knowledge to Himself."
However, this does not imply that these letters are meaningless or that they do not serve a clear and discernable function for those who read and listen to the Qur'ân. There is a general meaning that can be understood from all of the letters. These letters serve to highlight the literary nature of the Qur'ân.
Ibn Jarîr al-Tabarî, in his Tafsîr, gives us a survey of what early scholars of the Arabic language have explained about this stylistic device.
Some language scholars state that these are letters of the alphabet and that Allah suffices with them for the entire alphabet of twenty-eight letters...
Others say that the chapters begin this way in order to draw the attention of the polytheists - who had called each other to ignore the Qur'ân - so that when their attention was gotten, they would listen to what was understandable.
Others say these letters are a means of introducing the chapters. Allah begins his discourse by using them."
Alif Lam Mim- The Letters that Begin the Chapters of the Qur'an | IslamToday - English
Their best argument is that there are many explanations as to what they mean, but only they don't know which one.
I've read where it's a literary device, in much the same way as we end singing "Hey Jude" with na-na-na-na-na - that is; a filler.
However even this doesn't help, because there's still no consensus as to their purpose, only that they have some purpose!
Shaikh Abdullah Faisal says that there's 30 different explanations
AUTHENTIC TAUHEED: Notes: Alif Lam Mim- Shaikh Faisal
Against this there has been a surprising argument that they do have a definite meaning - based on alleged evidence on some site, or in some book.
It'd be a bit like me saying "I know this is true, if you don't believe me, go look in the library".