One of the specifications of engine oil is its viscosity grade, which is defined by standard SAE J300.

Multi-grade oils (such as 10W-30 and 15W-40) show both their cold and hot viscosity grades, meaning that they meet the performance criteria for two SAE viscosity grades.  The "W" in the viscosity grade means "winter".  SAE grades 0W-30, 5W-30, 10W30, and 30 all have the same viscosity requirement at 100°C.  Using 10W-30 for example, this multi-grade specification means that the oil performs like a 10W-weight oil at -25°C and like a 30-weight oil at 100°C.

Mono-grade oils (such as 30 and 40) meet only the performance criteria of a single grade.

Automotive Lubricant Viscosity Grades1
Engine Oils – SAE J300 (2015-01-20)

SAE
Viscosity
Grade
Low Temperature Viscosities High Temperature Viscosities
Cranking2 (mPa·s)
@ temp °C
Pumping3 (mPa·s)
@ temp °C
Kinematic4 (mm2/s)
@ 100°C
HTHS5 (mPa·s)
@ 150°C
max max min max min
0W 6,200 @ -35 60,000 @ -40 3.8
5W 6,600 @ -30 60,000 @ -35 3.8
10W 7,000 @ -25 60,000 @ -30 4.1
15W 7,000 @ -20 60,000 @ -25 5.6
20W 9,500 @ -15 60,000 @ -20 5.6
25W 13,000 @ -10 60,000 @ -15 9.3
8 4.0 <6.1 1.7
12 5.0 <7.1 2.0
16 6.1 <8.2 2.3
20 6.9 <9.3 2.6
30 9.3 <12.5 2.9
40 12.5 <16.3 2.96
40 12.5 <16.3 3.77
50 16.3 <21.9 3.7
60 21.9 <26.1 3.7

Notes

Item
Note
Dynamic viscosity μ 1 mPa·s = 1 cp, cp = centipoise
Kinematic viscosity ν 1 mm2/s = 1 cSt, cSt = centistokes
Viscosity Conversion ν = μ / ρ, where ρ is the fluid's density
Note1  All values, with the exception of the low-temperature cranking viscosity, are critical specifications as defined by ASTM D3244 (see text, Section 7).
Note2 Low-Temperature Cranking Viscosity, as defined by ASTM D5293
Note Low-Temperature Pumping Viscosity, as defined by ASTM D4684.
Note that the presence of any yield stress detectable by this method constitutes a failure regardless of viscosity.
Note4 Low-Shear-Rate Kinematic Viscosity, as defined by ASTM D445
Note5 High-Temperature High-Shear Viscosity, aka High-Shear-Rate
Viscosity
, as defined by ASTM D4683, ASTM D4741, ASTM D5481 or CEC L-36-90
HTHS is a measure of the shear stability of the Viscosity Index Improver (VII) additives of the oil.  Higher HTHS results in better film thickness thereby protecting bearings better, while lower HTHS results in lower fluid friction and therefore better fuel economy.
Note6 Applicable to 0W-40, 5W-40 & 10W-40 grades
Note7 Applicable to 15W-40, 20W-40, 25W-40 & 40 grades