Specific gravity is a measure of how dense your wort is. It's used to calculate the percent alcohol content of your beer (ABV) and helps us understand when our beer is done fermenting. Original/Starting Gravity (OG) is your wort's "potential" to become alcohol. Higher OGs mean higher possible ABVs. Final Gravity (FG) is the specific gravity achieved when the yeast are done doing their thing. The difference between OG and FG is used to calculate ABV. FG is also an important indicator of how well the yeast metabolized the sugars in your wort. If the number is too high, your beer will be unbalanced (i.e., overly sweet/malty because some of the sugars that were destined to become alcohol were not converted). When you see others using the term "attenuation", they are referring to how well the yeast did its job of converting sugars to alcohol and the CO2 bubbles we love to count.
The folks on this site are very good in helping new brewers identify why your OG may have been too low for a given recipe or why a FG may have been too high (incomplete attenuation). With respect to this latter point, it's important to know how people measure specific gravity. To follow up on what others noted, there is a difference between measuring your specific gravity with a hydrometer (a direct measure of specific gravity) versus a refractometer (which indirectly estimates specific gravity using light refraction). If you have both devices (and use them both), what you will see is that they are pretty close in their readings of OG (e.g., 1.048 vs. 1.050). At the end of fermentation, however, the measurements will be quite different (e.g., 1.016 [hydrometer] vs. 1.036 [refractometer]).
That's a big difference. One that makes you either do a happy dance (if you measured with a hydrometer) or panic that your fermentation didn't finish (if you measured with a refractometer). What gives? Well, in addition to sugars, your wort now has alcohol in it, and the alcohol changes the accuracy of the refractometer as a tool to measure specific gravity. Fortunately for us, others have worked out the equations to correct your FG.
Here's a particularly popular
tool for performing the calculations for refractometer readings. Note, it wants the values as Brix (not specific gravity). There's a
conversion calculator for that too.
In your example, you started at 1.065 (15.9 Brix) and ended at 1.036 (9 Brix) on the refractometer. Using the calculator, that equates to 1.017 as
@camonick noted above and matches what you measured with your hydrometer (1.016). Approximately 5.7% ABV.
Note...
1.036 FG on the refractometer does not always equal 1.017 when converted. You need to perform the calculation each time because the conversion depends on your OG. For example, if you have a high OG of 1.090 (Brix: 21.6 ) then a FG 1.036 would correspond to 1.008. Conversely, if you were brewing a Session IPA with an OG of 1.045 (Brix: 11.2), then a FG of 1.036 would correspond to 1.022. In the first example, there is more alcohol in the sample (10.1%) and this skews the refractometer reading more (it's off by 28 points) than the lower alcohol session beer (2.6% ABV; refractometer reading is off by 14 points).