Anime is a kind of film making, just as silent movies, talkies, color film, and 3D are. There are many different kinds of stories shown, and many different styles. Just as there are many kinds of styles of Hollywood movies -- drama, detectives, police, horror, mystery, comedy, romance.
What kinds of movies does she like, and is she willing to see what has been done in the anime medium? Some special effects are done better with animation, although sometimes the style is simplicity (I've seen one where people in the background become a cone and a circle).
See if she's willing to rent and watch the Studio Ghibli films which Disney has been distributing. I haven't checked which of these are available from Netflix, but if you use Netflix there is quite an anime assortment there. Some good series are also on Hulu, and Hulu is definitely not an anime-oriented site.
For that matter, if she's a Netflix user, you can search for a movie type and add "anime" and see what is suggested...find something she might like. Do the searching for her, so she doesn't have to wade through stuff she doesn't care for.
You can see summaries of many of these things on WIkipedia, so you can be prepared to discuss what you find interesting about the style, characters, culture, and plot.
Start with "Kiki's Delivery Service", as that is a very western environment. How does it compare to other stories about witches? How often do you see a witch learning? Why does that world accept magic users casually yet there are so few?
"Steamboy" is very western -- it ends up in London of a hundred years ago.
"Planetes" is the most realistic representation of space flight. They were careful to try to do the physics correctly. It's about space debris collectors. Really.
There's anime about many things. Basketball, baseball, roller skating, snowboarding, Adam-12 type of police ("You're Under Arrest!"), kids playing with robot dolls ("Angelic Layer"), a kid who is allergic to cats but has to help cats ("Nyan Koi!").
"Howl's Moving Castle" is entertaining, and I love the door. You'll know which door when you see it.
"Laputa: Castle in the Sky" is very popular.
Consider "Ah, My Goddess" on Hulu. It's a romantic comedy inspired by "Bewitched", and the situation is similar to "I Dream of Jeannie". Does your mother remember those, and how similar are those shows to this one? (The first episode is slow because they're showing us what kind of guy the boy is) Do you remember learning about the gods and mythologies of several cultures? Look up Belldandy's inspiration from a Norse goddess. Try to keep track of how many different mythological and religious and magical common beliefs and behaviors the creator has jumbled together...this is entertainment, not an attempt to follow a certain theology. Laugh and discuss.
Has your mother seen "The Addams Family" and did she like it? Also on Hulu is "My Bride is a Mermaid" (unfortunately, subtitled -- I think there are dubbed DVDs available). The first episode starts as if it is a retelling of "The Little Mermaid" story, but then things start going zany.
Many adults still enjoy Wile E. Coyote's chasing of the Roadrunner. On Crunchyroll.com, the 2010 show "Squid Girl" is available in subtitled form (free registration required). She's a squid who wants to conquer the world, but as an ignorant girl squid she has many problems.
Another Ghibli film is "Spirited Away", where a modern Japanese girl accidentally wanders into the land of the Shinto gods. That might be too japanese a movie, but if she has seen it and liked it, the short "Kamichu!" anime series (DVD only, I think) has a similar flavor -- a middle school girl realizes she became a Shinto god, and explores her new situation.
A very Japanese movie is "Princess Mononoke", full of great art but woven around hints of culture which is unfamiliar to we in the U.S. I watched it by just letting the story flow by as it unfolded. A good story, although as unfamiliar as the first time you heard of Hansel and Gretel.