Beer Gravity, How does it work?

Everytime I dream up a new question, I search through Homebrewtalk and if I dont find it, I find something similiar, then more questions pop into my head.

Gravity. How important is it? And how does it work?

I'm on my 5th batch overall. And 2nd cream ale.. in a row.
Both recipes asked for 1.040 OG and 1.010 FG.

My first cream ale OG at 1.040 and FG at 1.020. I let it sit for 7 days (I dont use a secondary yet). Bubbling was dead (not a peep after 3minutes) so I racked it to bottles. Should I have let it sit another 2 or 3 days? And if I did, and it was still 1.020, why? It turned out fine, but I was curious.

The second cream ale OG was 1.030 (its fermenting now). Why not 1.040? I began with 3 gallons while boiling the wort. 2gallons was left, I added 3gallons of fresh water. I'm thinking I should have went in after the trub a bit more. About a half gallon (trub and friends) was left in the kettle.

How do I mess with OG? Or should I. I did a hydrometer reading at the 4.5gallon mark, It appeared to be about 1.33ish, and at 5gallons it fell to 1.31ish. I think.

I figured its not a huge deal, but was curious as to how and why it works.

Thanks again guys

Gravity is important in that if we didn't have it we would float...oh, wrong gravity, sorry.

The hydrometer measures the weight of a liquid in relation to water. The gravity of water is 1.000. When you add sugars (malt) to the water the gravity rises with the increased measure of the sugar, more malt equals a higher gravity (1.060), less malt lower gravity (1.030).

In trying to decipher your situation, I noticed a missing key element - at what temperature did you take your gravity readings? This impacts your gravity.

The hydrometer is "calibrated" at 60 F (at least mine is according to the manufacturer).

At 60 F the measurement of your wort is basically 0.
At 70 F you have to add 1 (actually .001) - so 1.045 becomes 1.046
At 77F add 2
At 84F add 3
At 95F add 5
At 105 add 7

I usually only have to add 1 or 2.

Your gravity readings require a zeroing by recalculating the gravity reading IAW the temp of the brew. Once you do that I bet you will find the numbers are actually closer to your target gravities.

Good luck.

O' wise beer yoda,

Thank you again Bill.

Very much welcome you be young Brewwalker.