Might as well start with the definition and description(s)
here.
I've always said that the problem I have with davvening/praying in an Orthodox synagogue is not the mechitzah (gender-separation partition), but what doesn't go with it: In an Orthodox shul, a woman is not counted for a
minyan, not eligible for an
aliyah, and not permitted to lead services. (In
Women's Tefillah/Prayer Groups, which are women-led and for women only, those parts of the service for which a minyan is required are excluded; in
Partnership Minyanim, women may lead only those parts of the service for which a minyan is not required.) That said, the mechitzah itself can be a problem, depending on the synagogue's hashkafah/religious perspective, which does vary within Orthodoxy.
From the Wikipedia entry linked above:
"There are different views on the proper height of a mechitzah separating men and women in a synagogue. Differences about minimum mechitza height represent a source of disagreement between more liberal or Modern and more Ḥaredi Orthodox Jews. According to the
Shulchan Aruch HaRav, used by
Chabad-Lubavitch, a mechitza needs to prevent men from seeing a woman who might be immodestly dressed, and hence a mechitza needs to be as tall as a man, or 6 feet.
[7] However, according to Modern Orthodox Rabbi Ahron Soloveichik, a mechitzah need only serve as a halakhic partition, and hence need only be the minimum height for such a partition. Rabbi Soloveichik holds that this height is 10
tefachim,(each "tefach" 3.2 inches) about 32 inches is acceptable.
[3]."
There's a huge qualitative difference between being able to see and hear the "action," and davvening from behind a "Berlin Wall." There's also a huge qualitative difference between praying in a decent-sized ezrat nashim/women's section and davvening in what I once heard an Orthodox man describe as "the penalty box," an area so small that women who show up for shul are made to feel that they're being penalized for their efforts. And there are other considerations, as well. A former blogger once described her synagogue's ezrat nashim as a balcony with a wire-mesh screen above the front wall. While it's possible that the women could see and hear through the screen, I find the whole idea of praying in an ezrat nashim designed like a chicken coop downright offensive.
"In order to accommodate stricter interpretations and provide a way for women to see, many synagogues will make an opaque wall that is 3–4 feet high and add a lattice, screen, one-way glass, or other semi-transparent material above that opaque wall. "
That's one better way to go, and locals can see an example in Manhattan's Carlebach Shul. Another good way is to use ramps--the men descend a ramp into their section and/or the women ascend a ramp into theirs, ensuring that the women and men are clearly separated without cutting off the women's view. (Locals can see an example in Manhattan's Jewish Center). Or, for minimalists, there's the good old three-to-four-foot mechitzah. Orthodox Jews can't get around the requirement to have a mechitzah in a place of prayer, but I personally think it's preferable to ensure that women feel welcome than to insist that they be neither seen nor heard.
Here you can see photos of mechitzot, including mechitzot at s'machot/"simchas"/happy occasions. Why some Orthodox folks think that women and men must be separated even when they're not praying is a mystery to me.