Common symbols around you
Type of plastic (here 1, PETE), see also plastic numbers
Meets FCC's EM emission standards
double insulated, a.k.a. Class II
three variants of "safe to mount on normally flammable materials" (meaning things like wood and fabric(verify))
electrostatic discharge protection required
Some mark mentioning RoHS means it's compliant to RoHS
The top symbol is for DC barrel plugs, specifying whether the inside or outside is positive.
The middle line is input, where the squiggly tilde ~ indicates AC, here mentioning an input voltage range and frequency it's okay with (these specs amount to worldwide use).
The third line (output)'s solid and dotted line indicates DC.
LPS (Limited Power Source) have relatively low maximum voltage, current, and power. 
SELV (Safety Extra Low Voltage), where the power supply output stays safe under single fault conditions. 
Double circle, like a vertical venn diagram, are transformers, with a handful of properties marked. There are more combinations of all the parts this image shows, and further ones (e.g. construction site).
Some of the more commonly seen logos / certification bodies include:
UL (United States)
TÜV (Germany, international)
BSI, also Kitemark (UK)
There are actually many more testing centers, that may deal with additional health and/or safety and/or environmental concerns.
Many of these cover similar ground, but not exactly the same, and exist in part because laws and standards are partly country-specific. You're probably vaguely familiar with logos for your part of the world, even if you don't know what they mean.
Certification marks, represent agreements between manufacturers and (ideally well known) testing centers.
Note that there are also logos that do not mean that at all.
Whether certification marks are strictly required for sale varie(verify), but even when it isn't it may still be common, for a collection of reasons, like some individuals preferring safety-tested versions for certain products, liability in terms of insurance, varied indirect regulation (e.g. electrical code, fire regulation, medical safety) meaning certain businesses/resellers only buy certified devices, or even just self-imposed regulation like you caring more that your house/business is less likely to burn down.
Some devices are interesting cases. For example, power supplies are often separate from the devices they power, for practical reasons: e.g. when a large company that has locked down the design so that they can mass produce it, for worldwide sale, without a lot of new certification (certifcation is slow, sort of expensive, and may need periodic recertification) - and, separately, simplify the certification for all the brand's devices it may power because the power supply is no longer part of it.
That's also why power supplies have more-than-usual certification marks on them, including ones not required for your area.
Best known among them is chinese producers just stamping on the european CE mark.
Often with different, tighter spacing, presumably to to have an argument it's not the same. But note that this tighter spacing is also used in some actual CE products, just for space reasons.
This one has been nicknamed "chinese export".
A bunch of markings used around mechanisms, indicators, and buttons, around cars, audio, production lines are settled in ISO 7000 / IEC 60417, see e.g. See https://www.iso.org/obp/ui#iso:pub:PUB400008:en
IP ratings for water and object safety