The sodium part of table salt (NaCl) has consistently been implicated as a factor in the pathogenesis of essential hypertension, and a reduced salt intake is reliably shown to reduce blood pressure in people suffering from mild to moderate hypertension.
The required intake of sodium per day is around 25 mmol, a typical western diet contains around six times that figure (and many eastern diets contain even more sodium). Thus, since excessive sodium can cause or aggravate hypertension, and since we definitely consume too much of it, it seems reasonable to make an effort to limit the amount of sodium we consume each day.
If you speak to your doctor about reducing your salt intake, he or she will probably advise you to refrain from adding salt to your meals - either during the cooking process or just before eating it. This is good advice, and the downside is rather negligible. After initially missing the salty taste, people's palates soon readjust and they often even report noticing the other flavours more than before.
But that's the easy part. Unfortunately, the salt that we add to our food only constitutes (by one study's reckoning) about 15% of the daily sodium intake. Where does the rest come from? From a variety of sources, but the number one culprit, by far, is... (drum roll)
... the sodium added to food during its processing. This goliath of the salt world accounts for almost 60% of the sodium passing by our lips each day. For instance, the bread that you buy at supermarkets has almost 200 times the amount of salt in it than the wheat from which it is made.
What this means is that if you are keen to reduce the salt in your diet, you actively need to start reading the nutritional labels on food packaging. Simply shunning things that taste salty isn't good enough, because that taste is often masked by sugars and other seasonings. A case in point: cereals contain much more salt than salty peanuts, yet in the former instance the other flavours hide any salty sensations, whereas in the latter case the salt is unmasked and entirely on the outside, making it easy to be detected.
In my opinion though, these efforts are worth it. If successful, they can allow you to take fewer medications, and at lower doses, and in mild cases of hypertension, reducing your blood pressure in this fashion can obviate the need for any medication at all.