It does get better, but the hole never closed. For me on a day-to-day basis, I'm good. I can talk about my mother's passing without getting upset. The things that make it better is that she's just always a part of what I do. For instance my sister and I were shopping the other day and we saw a dress that my mother would have loved. My sister and I said "that's a mommy dress" and talked about how she'd be plotting as figuring out when and where she could wear it. It's the same for food she may like,things she would be happy about. We know she's with us in spirit. She truly was an awesome mother, sister and friend and just knowing the love she put out and the love she received from people and people still three years later talk about what a good person she was and how they deeply miss her makes it easier.
On the flipside, because it's not all puppies and rainbows, there are songs that set me off, mother's day is hard, the anniversary of her death is hard. No matter how much you tell yourself you're not going to cry, be sad, etc for xyz milestone day, you do. It's like a magnet and you get pulled in.
My experience losing my mother has been very similar to orangeblossom's, though it has been fifteen years for me, not three. I noticed by about a decade out that things were appreciably "easier." I still wish she wasn't gone, but I am okay with it now. I think of it like a gash in the forest... the scar is still there, but new life/growth is beginning to alter the landscape.
You've gotten great advice already, and I really can't add anything more. August 19th was the three year anniversary of my dad's death, so I understand what you're going through. Even though my dad was so sick and told us himself that he was ready to go, I wasn't ready for him to go. I still miss him like crazy and cry from time to time but I'm more likely to get mad, just completely mad that he's not here to share things with, that my kids (and nieces and nephews) didn't get enough time with him, etc. However, it definitely gets easier to smile when I remember something happy about him, and I love having dreams about my dad. So far all of my dreams of him have been about us traveling together, which is cool since we did travel a lot together when he was alive.