It is just an idiom. There is no real difference in meaning, but it is used much more often in writing (especially in fiction) since we tend to leave out unnecessary words in speech. I think it works better with long periods of time. I would hardly say 'много дней тому назад', but might say 'много лет тому назад'.

Fascinating! I didn't know this. Thank you for informing me about the etymology of this word ))

“Тому” it is a ukrainianism (a word or phraseological unit, as well as syntactic and grammatical construction of the Ukrainian language used in another language, in this case in Russian language). In modern Ukrainian language we often use this word and construction: “Вона прийшла 3 години тому” (Ukr.) = “Она пришла 3 часа тому назад” (Rus.) = She came 3 hours ago (Eng.) This word indicates the time elapsed from any action, event, state, in which someone, something was by the moment of speaking about them (in combination with words indicating a period of time). Basically, for translation, it is an equivalent of “ago” in English language. This word is often used in Ukrainian everyday speech but in Russian language it is mainly used in writing. While studying Russian language you have to remember that in fact it is a mixture of languages. Russian language is a combination of several languages: old Church Slavonic + old Turkic (old Tatar languages) +old Finnish + old Ukrainian (the language of ancient state Kievan Rus: modern Ukraine, Belorus and Lithuania lands) and other borrowings from European languages (French, German, etc.) So when you find a strange word or a grammatical construction in modern Russian language you may search for the roots in old Turkic, Finnish, Ukrainian, Greek and other languages (French, German, etc.)

Thank you both very much) I think I get it now a little better

Literally: "TO THAT what I am saying about".