As others have stated, "парень" really just means "guy" or "lad." There is no explicit word for "boyfriend" in Russian. So, the phrase "твой парень" is really just like saying "your man" in English. Oddly however, there is an explicit word for "girlfriend" which is "подруга" or "подруша." Although, this can also be used interchangeably among female friends, like in English.
What's the point of the ь? If you look at the word with the English letters they use an apostrophe and I haven't heard them pronounce it (admittedly my ear is not the most trained one around) so does anyone know what it's for? Is there something it's supposed to sound like that I'm missing?