Does anyone know what does the "feat." mean exactly?
Some song titles have the word "feat" in it, for example "I wanna love you clean Akon feat. Snoop dog".
What does "feat." mean?
Just featuring. This is used when there is an invited artist on a track.
It is not restricted to music. It was used on film and show billboards. You could also translate this (depending on context, select as many options as appropriate) by
with the (exceptional/gracefully acknowledged/reciprocated/just-passing-by/I-just-so-love-this-guy/requested-by-the-management/i-lost-a-stupid-bet/this-is-my-brother-in-law) participation of
to use a latin-derived word.
This is also very common for songs put out by DJs and Producers to identify the vocalist but to not credit the song to them. For instance, you have "When Love Takes Over" (feat. Kelly Rowland) by David Guetta rather than "When Love Takes Over" by Kelly Rowland. This could easily be the identical song, just credited differently.
It means "featuring".
Like for the example you gave, Jay Z will be singing the song, and Linkin Park will have a little segment/part in it. It can be during the song, or just one part.
You hear a TON of people have a little rap section in the song, so that's why you see a lot of "feat. T-Pain" and "feat. Jay Z"
PS...if your song is '99 Problems'(the Jay Z feat Linkin Park one), I think it's actually "Linkin Park feat Jay Z"
Hope that helps!