I can say, as a salt snob, that sea salt is a far more flavorful product.
I can't even use regular table salt anymore.
Sea salt is salt formed from evaporated sea water, is not iodized, and because it doesn't come from salt mines requires very little processing.
Some people will say that because it's "natural", sea salt must be better for you.
The mayo clinic seems to disagree: http://www.mayoclinic.com/health/sea-salt/AN01142
cooking.stackexchange.com/users/99/Mike Sherov
Iodine.
Table salt has added iodine, and sea salt doesn't.
Sea salt also tends to be a little coarser, but that's just cosmetic.
Sea salt isn't as refined as table salt, either, so it may contain traces of other minerals (magnesium, sulfur).
Sea salt is also considered to be kosher.
cooking.stackexchange.com/users/218/Satanicpuppy
As mentioned by Satanicpuppy , sea salt is largely regular, uniodized salt but with small amounts of different minerals from ocean water , and without the anticaking agent added to salt.
So, at least chemically , they are very similar as sea salt is still ~85% regular salt.
The presence of different minerals affects the taste and texture (maybe someone who uses it a lot can tell you how).
You can also find iodized sea salt sold in case you want to substitute it completely for normal iodized salt.
cooking.stackexchange.com/users/94/Kryptic
It depends on what country you come from.
In many countries "table salt" is just their local sea salt, crushed, filtered, and sometimes iodized.
Not every country has "salt mines", but most countries with a coast line can collect or "farm" evaporated salt.
See this PDF
cooking.stackexchange.com/users/3203/TFD
In Italy we basically only use sea salt, in Romania they use mostly rock salt.
Once the salt has been mixed into the food, I can't tell the difference.
I don't taste salt by itself because... you would have to pay me for it.
Of course, if you did an A/B double blind test, perhaps you would get some effect.
But do you care?
Healthwise, food safety agencies the world over seem to have no problem at all with rock salt and sea salt.
Somebody befor ementioned iodine -
that is something to keep in mind.
cooking.stackexchange.com/users/4558/Walter A. Aprile
I often sea sea salt sold in grinders to be used at the table, with comments about how it tastes better. What sort of taste differences would I notice using sea salt vs table salt, and what other differences might using one over the other impart?  I've also noticed people say that regular table salt is unhealthy, but that sea salt is somehow healthier for you.
What is the difference between sea salt and regular table salt?
cooking.stackexchange.com
<salt>
cooking.stackexchange.com/questions/788
cooking.stackexchange.com/users/123/Ryan Elkins
Sea salt is taken from evaporated seawater rather than salt mines, so it undergoes less processing and doesn’t have added iodine and anti-caking agent. Sea salt may taste better, but some do not notice the difference in a meal. There are mixed opinions on whether you can actually taste the difference. Table salt contains additives whereas sea salt is completely natural.
Sea salt is more flavorful than table salt. Table salt contains iodine and anti-caking agents, whereas sea salt receives very little processing. In food, it is difficult to tell the difference.