If you've ever knitted even one stitch, you know that the size of the needle determines the size of the stitch. Bigger needles make bigger stitches, smaller needles make smaller stitches. That's why needle size matters.
What may not be so obvious, however, is that once you've knitted the stitch, that stitch will not change shape or size, even if you later manipulate it using a different size needle.
"Huh?" you might ask yourself "what is that woman talking about?" Well, I'm glad you asked.
In the photo above, the left needle is smaller than the right needle. But because the stitches were made with the right needle, a smaller left needle won't affect the gauge or the tension.
Still confused? Here are three real-world examples.
Suppose you are a dreadfully tight knitter. No matter how you try, you cannot relax your tension. The stitches are hard to push around. Knitting exhausts you.
For circular knitting, at least, you can solve this problem without brandy.
Buy an interchangeable knitting needle kit--a packet of interchangeable tips which fit on a series of cables of all sorts. Screw the tip you need for your gauge onto one side of the cable. Holding this tip in your right hand, use it to knit-- to create the loops which become the "new stitches." Screw a much smaller gauge needle onto the other side of your cable. Holding this smaller tip with your left hand, use it to feed the "old stitches."
Because the left "holding" needle is so much smaller than the right "creating" needle, the stitches will easily slide around, and your tight tension will be at least half-tamed. This trick works because, once you've created the stitches using the right needle (the one at the proper size for your gauge), you cannot change the size of those stitches by knitting them off a smaller left needle.
Another example: Suppose you've made a mess on a complicated knitted fabric of some kind--a lace scarf for example. You now want to rip back to some point before you made your mistake. You would locate a plain row, and without ripping back anything for the moment, you'd pick up the stitches of that row on the very thinnest needle you can find. Once those stitches are safely on the very thin needle, remove the needle used to knit the lace, and rip the lace back, past the mistake, to where the plain row is impaled on the thin needle.
Once you've ripped back and have the stitches of the plain row sitting there, you can knit those stitches right off the thin needle--no need to transfer those stitches onto a larger needle. As long as the needle doing the knitting is the needle size used to create the lace in the first place, the size of the "holding needle" will not change the size of the stitches.
Final example: Stitch holders are a much smaller gauge than the actual needle used to produce the stitches being held. Most knitters transfer the stitches from the stitch holder back to a needle before knitting further. But there is no reason to go to all that trouble. If the design of your stitch holder allows, no harm will come to your gauge or tension if you knit the "held stitches" right off the stitch holder, as long as the needle doing the knitting is the correct gauge.
The moral of the story: In knitting, all the matters is the size of the needle DOING THE KNITTING (the right needle). The size of the holding needle (the left needle) DOES NOT MATTER.
(Mirror image knitters: if you substitute "right" and "left" in all of the above, everything remains true)