Welcome to KH! You've come to the right place if you want to improve your knitting skills! This is a great forum - the best! - filled with knowledgeable and skilled fiber artists! And also there are lots of beginners and in-between'ers who are just starting to explore this wonderful art form.
About gauge - Think of it as a matter of size. If you and I sit down to knit right next to each other, using the exact same yarn and the exact size needles, odds are that when we finish our sample piece of work they won't match exactly in size.
Suppose we started with 60 stitches of worsted weight wool on size 8 (US) needles and knitted back and forth in stockinette stitch (one row knit, next row purl, then repeat). Let's knit a piece about 6 inches long and then bind it off.
So here we sit with our little squares and it's time to measure - how many stitches did it take to measure 4" across and how many rows did it take to make 4" lengthwise.
I knit rather loosely so I got 24 stitches and you knit a bit tighter so you got 28 stitches in 4" across of your little sample. Translated to gauge terms, I knit 6 stitches to the inch (24 divided by 4") and you knit 7 stitches to the inch (28 divided by 4"). (We're primarily concerned with how many stitches across 4" rather than how many rows in length.)
Now, the guy or gal who wrote the pattern, sitting next to us and using the same yarn and needles, is going to get his or her own results that may or may not match ours. Perhaps the author of the pattern knits like you do and gets 7 stitches to the inch.
That being the case, I'd have to adjust my knitting to match the pattern writer's "gauge" so I could get the same size stitches as the author's. Otherwise the garment the pattern is written about won't fit. So I would adjust my needle size until I, too, were knitting 7 stitches to the inch. Then, when I go to knit the garment, if I want to make the "medium" size described in the pattern, it will come out to fit because I match the pattern writer's stitch size or gauge.
Machine knit garments aren't even in the same universe as hand knit ones when it comes to gauge systems. They have their own laws and rules while having only a slight connection to the world of hand knits. So just remember that the writer of the pattern is the leader gauge-wise and the knitters follow the leader to get the sizes right!
Good luck and let us know how it goes!