Gravity: what's the deal with this?

Honesty time…
I have been brewing for almost a year (mostly small batches until recently) and I have no idea what the gravity is supposed to mean.
If a beer is 1.062, what am I supposed to do if I test it and the reading is lower or higher?
From what I can tell, the reading is really only telling me how badly I screwed up.

Any help would be appreciated. I have a batch fermenting and I was told to look for 1.052 or 8 and I’d like to know what I’m supposed to actually do if it’s high or low.

See if this helps.

http://www.howtobrew.com/appendices/appendixA.html

Gravity is just a theory, it is not proven. Another explanation could be that the earth just sucks.

In brewing, gravity is a measure of how dense the wort is compared to water. A wort that has a gravity of 1.050 is 5% denser than water. 1.056 is 5.6% more dense. What makes that useful is that sugar is the primary component of wort that changes the density. Thus, you can consider gravity to tell you how much sugar is in the wort, and consequently how much alcohol you will end up with after fermentation.

If you are off by several gravity points, that just means your final alcohol content will be off by a relative amount. Generally not something to worry about. Where this can get really useful though is taking a reading at the end of fermentation. That will tell you if the yeast are done and if it is safe to bottle.

That explanation and link were helpful.
Thanks!

You mention moving to larger batches recently. Extract? If so, one thing to watch for is that you can get wildly bad gravity readings due to incomplete mixing of the top-off water. It’s not a missed OG, it’s a bad reading.
With extract, you’re pretty much guaranteed to hit the mark, +/- 0.005 I’d call it close enough. Much more, just stir some more and read again. Or just say “it’s extract,” and have faith you hit the target OG.

Also specific gravity readings are temperature dependent. As you take a reading take the wort’s temperature too. Use an ABV calculator that accounts for temp.

Assuming your volume measurements are accurate, and you don’t leave too much sugar with the trub in the kettle.