Despite its apparent length paragraph 10 of Section 263 is comparatively simple to understand. It is concerned with the defining moment when the strictures of Shabbat begin and all melakhah is forbidden. (For an explanation of this rather enigmatic Hebrew word see Shabbat 008.) In North Africa in the 9th century CE Rabbi Shim'on Kayyara in his halakhic compendium "Halakhot Gedolot" determined that from the moment the candles have been lit all the strictures of Shabbat apply, even though the hour might be some considerable time before the onset of twilight. Furthermore, according to Rabbi Kayyara, this ruling would apply to all the members of the household and not just to the person lighting the candles.
In the 13th century, in western Europe, this idea of Rabbi Shim'on Kayyara was taken a stage further. "Shibbolé Leket" is a compendium of responsa edited by Rabbi Tzidkiyah Anav, and in this work he brings the custom whereby after having lit the candles women discard the burning match without putting it out because on Shabbat it is forbidden to extinguish fire. (Actually, he refers to the women discarding a burning wick, because of course at that time there were no matches: I have modernized the concept for a more simple understanding.)
But not all halakhic authorities took this view. A collection of glosses on Rambam's great "Mishneh Torah" reflects the views of the Ashkenazi scholars of western Europe. This work is called "Hagahot Maimoniyot" [Maimonidean Glosses] and was compiled by Rabbi Me'ir ha-Kohen, a student of Rabbi Me'ir of Rothenberg. Thus these glosses reflect the ideas of the Tosafists. (Rabbi Me'ir ha-Kohen died in the Rindfleisch massacre of 1298 CE.) The "Hagahot Maimoniyot" are of the opinion that when lighting the candles a woman may make a reservation that by doing so she does not accept upon herself the sanctity of Shabbat and will only do so a little later at the same time as the rest of the community does in the synagogue.
It seems reasonably clear that this dichotomy of halakhic opinion derives in no small measure from a differing philosophy concerning the lighting of the candles. The tradition emanating from North Africa seems to view the lighting of the candles as a sacred ritual and that once the benediction over lighting the candles has been recited all the laws concerning Shabbat must immediately take effect. The tradition emanating from the Tosafists seems to view the lighting of the candles as a preparation for Shabbat; a preparation during which the housewife makes sure that there will be light in her home during the Sabbath eve so as to ensure "Shalom Bayit". According to this view, while a woman would usually apply to herself all the Sabbath restrictions after lighting the candles she may also make a reservation that by lighting the candles she is not assuming the sanctity of Shabbat, which is something that will apply to her only when it applies to all the rest of the congregation.
This "discussion" leads Rabbi Karo to the question of when Shabbat actually begins for the general population of any given community of Jews. What he says makes two unmentioned assumptions. These assumptions are not mentioned simply because in his time - indeed throughout the middle ages - they were taken for granted. Since our customs today differ, we cannot take these assumptions for granted and must explain them. The most relevant assumption is that on Erev Shabbat the congregation will hold its evening service while it is still daylight. (Indeed, this was the case on every day of the week during the middle ages, and not just on Friday night.) Provided the service was held some time after Pelag ha-Minĥah Shabbat would begin for the whole community when the cantor began to intone Barekhu, the invitation to public prayer. The second assumption that must be articulated is that we are dealing with a close-knit community of Jews and that there is only one synagogue which is attended by all the Jews of the community. Accordingly, when the cantor begins the invitation to the Evening service Shabbat begins for the whole community and everyone must be obliged by the restrictions of Shabbat from that moment on. (This would mean that a woman who had lit her candles earlier would be able to make the reservation that she would accept the sanctity of Shabbat only when everyone else did.)
In his note, Rabbi Moshe Isserles obviously emphasizes the Ashkenazi tradition: a woman is bound by the strictures of Shabbat from the moment she lights the candles unless she makes a specific reservation that she does not do so, but will accept Shabbat together with all the rest of her community. He adds that this reservation does not have to be actually articulated, and it is sufficient that the woman makes a mental reservation before lighting the candles. Furthermore, he adds, the fact that the candles have been lit does not mean that Shabbat has necessarily begun for all the other members of the household even if it has begun for the woman who has lit them: they may wait until Barekhu is recited in the synagogue. (Actually, as Rabbi Karo notes, we now preface Psalms 92 and 93 before Barekhu, so Shabbat begins for the community when those Psalms are recited.)
Before continuing to explicate Rabbi Isserles' note I think it would be helpful if we summarize the law as it may be applied in our congregations today. We no longer accept that Shabbat begins with the recitation of Barekhu (or Psalm 92) in the synagogue for many reasons: in each community there is more than one synagogue and they do not all hold their services before dark. (And even where there is only one synagogue they do not always hold their service at the same time: in the winter they may well hold the service after dark while in the summer they will hold it before dark.) As we have noted on several occasions it is now universally accepted that Shabbat begins a certain number of minutes before sunset (in most places that certain number is 18). Therefore, a woman must light her candles before that time (and may not do so at all after twilight has begun) and Shabbat will begin for all the members of the household at the very latest those few minutes before sunset.
With the introduction of electric lighting the kindling of the Shabbat candles has gradually lost its utilitarian aspect (of providing light and warmth in the home) and has become a sacred ritual for almost all women (and men) who light candles. It therefore seems to me that we should abide by the view that we accept upon ourselves the sanctity of Shabbat from the moment that the candles are lit and thereafter avoid any meelakhah.
Rabbi Isserles adds one more proviso: once the Sabbath candles have been lit they may not be moved. Indeed, they and their holders are what we term muktzeh: they are 'set apart' as 'not for use' and may not be touched or moved throughout Shabbat. While candles may be lit throughout the house the essential place for them is where the family will eat its Sabbath meal. It is on these candles that the benediction should be recited, even if candles are lit in other rooms as well. It is probably because of this consideration that the custom grew up of placing the Shabbat candles on the dining table, so that they may shed their light for the diners. However, in many halakhic circles it was suggested that the candles should not be placed on the dining table, but on a side table, so that if it should be necessary during Shabbat to move the table this would be permissible. (As long as the candles and their holders are on the table the table may not be moved even after the candles have gone out. This is because the table is a base - support - for something which is muktzeh - the candles - and partakes of their halakhic properties.)