The Mass Effect trilogy has been my favorite story told across any medium for the last 7 years. Legendary Edition was my 14th playthrough of the trilogy. Seeing ME1 with the graphical updates was amazing. It still has that 2007 vibe, but it looks a lot less dated. 2 & 3 were already gorgeous games, so you may not notice as big of a change with these two as you will with ME1. However, the cutscenes in 2 & 3 look absolutely gorgeous now. Blew me away every time. ME:LE also comes with all the DLCs, so you won't have to shill out an extra $50+ to get some incredible stories that expand on the main story very well.

If you don't already own the trilogy, cop this ASAP. It's the definitive version of one of the greatest stories ever told and you should absolutely experience it.
If you do, with Legendary Edition you'll get some phenomenal graphics updates and all the DLCs if you didn't have them already.