it's something we instinctively know once hearing an explanation. it's obvious to me so my explanation might not be the best.
but i'll try explain it to you and hope i explain it well enough that you understand

in 3D space there is the x axis, y axis and z axis (you should have heard of x and y before in math class when you started high school at least.. provided they still teach that stuff when you went)

in the case of maya x points from left to right
y points from down to up
and z points back to forward

a plane is a flat surface

a coordinate for a point (vertex) is something like this: (x, y, z), where x, y, and z are real numbers (there are such things as imaginary numbers but you dont need to worry about that) and represent the space that the point is in. so a point at (0, 0, 0) is directly in the middle of the world

in the attached picture i have 3 planes
the red plane's verticies are all on the 0 coordinate of the x axis. it is on the y-z plane because all of its points have a 0 coordinate in the x.

the green plane's verticies are all on the 0 coordinate of the y axis so it's in the x-z plane.

the blue plane's verticies are all on the z coordinate of the y axis so it's in the x-y plane

in the second part of the attached image the arrows point in the positive direction.
to 'mirror' something in a x-y, y-z, or x-z plane is to make of copy of all the verticies of the object
you mirror something in the negative y-z plane then you take the object's verticies and you (for lack of better word) translate them to the other side of the y-z plane


if you don't understand what i said then that's because it's obvious to me after seeing the 3 planes and knowing which way the axis are going (and it might be to you once you know what just happened)

but i hope you get the idea of what i said...

if you don't get it then just bash the buttons away until you get the result you want (i do that most times)!