Another good intelligent discussion started. I'll try and explain it to you from my point of view, because I enjoy the genre, most of the time anyway.
When you're watching shows like TTGL, they are amazing and really fun to watch, but can it really be related to your own life? I'm not going to gain spiral energy and drill through the earth tomorrow. When it comes to slice of life, you feel you can really connect with the characters and share their feelings, as due to the realistic setting you can understand them better. They often delve more into the characters personalities and you can end up being quite attached to the characters. But don't get me wrong, I'm talking about the
GOOD ones. There are some really shit ones out there also. Harem ones tend to be bad 90% of the time due to bad endings.
Good Slice of life:
Toradora!
Itazura na Kiss (especially good for me, seen as it followed the characters through to my age and beyond, and I'm training to become a doctor like one of the characters in it

)
Beck
Skip Beat!
Well there ya go.