The -geometry option controls the size and position of the initial Emacs frame. Here is the format for specifying the window geometry:
Specify window size width and height (measured in character columns and lines), and positions xoffset and yoffset (measured in pixels).
This is another way of writing the same thing.
{+-} means either a plus sign or a minus sign. A plus sign before xoffset means it is the distance from the left side of the screen; a minus sign means it counts from the right side. A plus sign before yoffset means it is the distance from the top of the screen, and a minus sign there indicates the distance from the bottom. The values xoffset and yoffset may themselves be positive or negative, but that doesn't change their meaning, only their direction.
Emacs uses the same units as xterm does to interpret the geometry. The width and height are measured in characters, so a large font creates a larger frame than a small font. (If you specify a proportional font, Emacs uses its maximum bounds width as the width unit.) The xoffset and yoffset are measured in pixels.
Since the mode line and the echo area occupy the last 2 lines of the frame, the height of the initial text window is 2 less than the height specified in your geometry. In non-X-toolkit versions of Emacs, the menu bar also takes one line of the specified number. But in the X toolkit version, the menu bar is additional and does not count against the specified height. The tool bar, if present, is also additional.
You do not have to specify all of the fields in the geometry specification.
If you omit both xoffset and yoffset, the window manager decides where to put the Emacs frame, possibly by letting you place it with the mouse. For example, 164x55 specifies a window 164 columns wide, enough for two ordinary width windows side by side, and 55 lines tall.
The default width for Emacs is 80 characters and the default height is 40 lines. You can omit either the width or the height or both. If you start the geometry with an integer, Emacs interprets it as the width. If you start with an x followed by an integer, Emacs interprets it as the height. Thus, 81 specifies just the width; x45 specifies just the height.
If you start with + or -, that introduces an offset, which means both sizes are omitted. Thus, -3 specifies the xoffset only. (If you give just one offset, it is always xoffset.) +3-3 specifies both the xoffset and the yoffset, placing the frame near the bottom left of the screen.
You can specify a default for any or all of the fields in .Xdefaults file, and then override selected fields with a -geometry option.