The Torah states that all Korbanos must be accompanied by an offering of salt (ויקרא ב:י"ג). Based upon a Posuk in Yechezkel (מ"א:כ"ב), the Gemara in Berachos (דף נ"ה.) indicates that as long as the Beis HaMikdash stood, the Mizbeiach effected atonement for the Jewish people; now, in the absence of the Beis HaMikdash, a person's table effects atonement for him. Although silent here, Rashi in Chagigah (דף כ"ז. בד"ה שולחנו), where this same statement appears, explains that the atonement effected by one's table comes about through the Mitzvah of הכנסת אורחים, inviting guests to join one at his table. Tosafos there (בד"ה שלחנו), referring to a Gemara in Sanhedrin (דף ק"ג:), allude to the importance of the friendship that can be established when one shares food with guests. This statement appears in the Gemorah in Menachos (דף צ"ז.); Rashi there (בד"ה שולחנו), as ammended by the Shittah Mekubetzes (שם אות ט'), seems to say that the atonement is effected by one's readiness to share one's food with a poor person. Whatever the exact comparison is, it is clear that Chazal understood that one's table is somehow to be compared to the Mizbeiach.
The Gemara earlier in Berachos (דף מ.) rules that one cannot make Hamotzi and eat bread unless there is salt (or some other relish) on the table, a ruling accepted by the Shulchan Aruch (אורח חיים סימן קס"ז סעיף ה'). The Shulchan Aruch continues to explain, though, based upon the conclusion of the Gemara (שם), that this is necessary only for inferior quality bread which does not taste good without some additional flavor like salt. But if one is eating most types of bread that we have today, which are tasty without salt, one need not have salt on the table. The Ramo, however (שם), writes that based on the aforementioned equation between the Mizbeiach and one's table, it is proper to always have salt at the table, regardless of the type of bread one is eating. The Ramo asserts that actually השלחן דומה למזבח, the table is similar to the Mizbeiach, and האכילה לקרבן, the eating (at the table) is similar to the offering of a Korban. Just as, therefore, the Posuk in our Parsha states that one must offer salt with every Korban brought to the Mizbeiach, so too one must have salt whenever eating bread at one's table. It is thus our practice to always have salt at the table at the start of the meal.
The Ramo (שם) then adds that the presence of salt at the table protects one from danger. This idea is quoted by Tosafos on the above Gemara in Berachos (דף מ. בד"ה הבא), where a Midrash is cited, explaining that when people sit at the table (silently) waiting for everyone to finish washing for Netilas Yadayim (so that the head of the household will then recite the Beracha of Hamotzi for everyone together), they are unable at that point to perform any Mitzvos. They are thus susceptible at that moment to danger since they are unprotected by Mitzvos. It is the salt at the table which then protects them at that time because, as the above quoted Posuk in our Parsha states, Hashem has established a special covenant with salt; this covenant somehow assures that no misfortune will befall the people at the table. Some suggest that because of this, the Ramo (או"ח סימן תע"ה סעיף א') rules that on the first night of Pesach, which is described by the Torah (שמות י"ב:מ"ב) as a ליל שימורים , a guarded night, a term understood by the Gemara in Pesachim (דף ק"ט:) to imply that Jews are especially well protected from danger on that night (עיין סימן ת"פ סעיף א' ברמ"א וסימן תפ"א סעיף ב' ברמ"א), it is not necessary to have salt with one's Matzoh, because the protection is there anyway (עיין בספר הגדה שלמה מבוא פרק ל"ח אות ג' בשם לקט יושר). [There are, however, other explanations given for the Ramo's ruling, as advanced by the Chok Yaakov (שם סימן תע"ה ס"ק ד'), the Aruch HaShulchan (שם סעיף ה'), and the Mishnah Berurah (שם ס"ק ד'), all of whom connect it to the actual Mitzvah of eating Matzoh.]
It is interesting to note that the initial ruling of the Ramo cited above (סימן קס"ז סעיף ה') speaks only of having salt on the table when one eats bread; he does not say anything about eating the salt. Actually, the Ramo later on (סימן ק"ע סעיף כ"ב) does say that one should eat salt at the end of one's meal, but then he adds that since salt is a standard ingredient in bread and in other foods eaten at the meal, it is not necessary to eat salt specifically anymore. The Machatzis HaShekel (סימן קס"ז ס"ק ט"ו) explains, however, that although salt may be an ingredient in the bread or in other foods, one must still have salt at the table by itself because of the comparison between one's table and the Mizbeiach, as well as to protect one from danger, although one indeed need not eat it. The Magen Avraham, though (שם ס"ק ט"ו), quotes that the Mekubalim held that one should in fact dip the bread into the salt and eat it; the Be'er Heitev (שם ס"ק ח') and the Mishnah Berurah (שם ס"ק ל"ג) say to dip the bread into the salt three times before eating it. The Kaf HaChaim (שם ס"ק ל"ז) quotes several Kabbalistic reasons for having salt at the table, adding (שם ס"ק מ') that it is the woman's Mitzvah to put the salt on the table.
The aforementioned Gemara in Berachos (דף מ.) quotes one view that if after making the Beracha of Hamotzi, but before eating the bread, one realizes that there is no salt, he may ask that salt be brought to the table. This view does not consider this speaking to be an interruption because the salt is needed for the meal, and having it out on the table is thus necessary for the Beracha, as explained by Rashi (שם בד"ה הביאו). The Shulchan Aruch (סימן קס"ז סעיף ו') accepts this view, but the Ramo (שם) adds that לכתחילה, it is certainly preferable that one not speak, thus implying that לכתחילה one who has no salt on the table should, after having made Hamotzi, take a bite of the bread without salt, rather than interrupt by asking for salt before eating. It should be noted that contrary to popular belief, it doesn't matter whether the interruption is spoken in Hebrew or any other language; it is improper in any case. If, however, one has washed for Netilas Yadayim, but has not yet said the Beracha of Hamotzi, one may then even לכתחילה ask that salt be brought to the table because it is needed for the meal, and, although the Shulchan Aruch (סימן קס"ו סעיף א') rules that one should avoid speaking between Netilas Yadayim and Hamotzi, the Mishnah Berurah (שם ס"ק ב') explains that speaking about anything needed for the meal is not considered an interruption at that point. Again, the language one speaks in does not make a difference.
Based upon the above cited comparison between one's table and the Mizbeiach, the Aruch HaShulchan (סימן קס"ז סעיף י"ב) notes that one may not do anything disgusting or inappropriate at the table, because it would be disrespectful to do such things by the Mizbeiach. The Mishnah Berurah, in the Shaar HaTziyun (שם אות כ"ה), observes, based on a Mishnah in Pirkei Avos (פרק ג' משנה ד') which quotes the above Posuk in Yechezkel, that another reason one's table effects atonement for him like the Mizbeiach is that people speak, or should speak, Divrei Torah at the table.