When my mother gave it to me, it was doing pretty bad. Now it's doing a lot better, but I'd like to know what kind of plant it is, any ideas?
Certainly appears to be a Spathiphyllum but determining a species would be impossible from a photograph. The common names are Spath, Peace Lily, and Snow Flower. There are a very large number of species (close to 100) in this genus along with at least 100 additional hybrid variations. Almost all sold in the U.S. are hybrids. The plant is an aroid which simply means it produces a spathe "flower". That "flower" is not a flower at all, but instead is a modified leaf. These plants do well in moderate light but they don't appreciate being over watered. In most cases, water it when the plant indicates it is "thirsty" by beginning to droop the leaves. Originating on the fringes of tropical rain forest regions, it needs warm temperatures. Give it a loose soil that drains very quickly and will not stay soggy. Overwatering is the primary reason many of these do not survive. With good care and limited water they will grow for many years. If you use the search at the top of this forum for Spathiphyllum you can find quite a number of discussions regarding the care of this plant.
It's a Dieffenbachia that looks worse for wear. http://tomorr.tripod.com/thegreenhouse/dieffenbachia/dieffenbachia.html See bottom of page. (Results of bad lighting) HTH Chris
I believe you are absolutely right!! I didn't pay much attention to the second photo until you made this post. When I copied it, blew it up in PhotoShop and examined the cane, I could see the traits of Dieffenbachia. Good catch! Still in the aroid family, but not a spath.