Well, you have tell Illustrator what sized page you're printing to, but your printer won't be able to print right up to the edge of a piece of paper, it'll stop a few mm short of the sheet edge so you don't get ink (or toner or whatever) all over the internals of your printer. So it'll have an imageable area a bit smaller than the page dimensions.
Now, set it to print with tiling switched off, and you can see this area with the page tool. You can make changes to the print setup and hit 'done' instead of print to check your setup before you commit to printing. The page tool is on a flyout with the hand tool, on the bottom left of the main tool palette - it looks like a rectangle with a little plus sign in the corner. Select this tool, hold down the left mouse button, then you can drag a page guide around your artboard to set the print area - the outer rectangle is the page edge, the inner rectangle is the edge of your printer's imageable area.
Now, you could manually print several pages like that, manually moving the print area each time, or you could select 'tile full pages' or 'tile imageable areas' in the setup section of the print dialog box. If you do that, the page guide you can move around with the page tool turns into a grid of pages.
'Tile imageable areas' will print the entire artwork, but you'll have to trim the edges of your printed pages down to discard the non-printable border of each sheet in order for them to fit together properly, which can be difficult to do if you don't have graphics right up to the page edge.
'Tile full pages' will print everything in such a way that the artwork is correctly positioned when your printed pages are all taped together edge-to-edge, but because there is a non-imageable area at the edges of the page, you'll have white page border gaps running through your artwork - this sounds like what you've done, and it's often perfectly adequate for making paper templates and such without having to worry about trimming a few mm off of every page edge.