Seder Taharot opens with masechet Kelim, vessels, which at 30 chapters and 254 mishnayot is far and away the largest of the 63 tractates of the Mishna. To fully understand the masechet, one needs great knowledge of “realia”, understanding the day-to-day of life during the Temple period—specifically, the types, sizes and shapes of various vessels in use throughout the Mishnaic period. The focus of the masechet is defining exactly what is and is not classified as a kli, and thus, susceptible to the laws of tumah.
While this was extremely important and practical during Talmudic times, today, beyond the laws of family purity, its most practical application likely relates to the schach of a sukkah. As one may recall, kosher schach must consist of material unable to contract tumah. Hence, the question of whether, say, a bamboo mat is considered a kli that is susceptible to impurity, mekabel tumah, and thus cannot be used for schach. Multiply that question a hundredfold, add in many a permutation such as the status of a vessel with a hole, one that wobbles, a vessel split into two, or is missing a leg, and one is ready to learn masechet Kelim.
Let us cite one small example. The 17th chapter of the masechet begins with the teaching that “kol kli ba’al habatim, all vessels used by a homeowner, their measure is a pomegranate”, meaning that if the vessel has a hole the size of a pomegranate, it loses its status as a vessel and can no longer contract tumah. Rabbi Eliezer disagrees and argues that the status of the vessel is determined based on its use. A kli used for olives loses its status if it has a hole the size of an olive; a vessel storing dates, if the hole is the size of a date; and so on and so forth. The Mishna further discusses the size of a hole needed to render a basket not in current use, baskets used by gardeners or by bathhouse attendants, no longer a basket. In a ruling that affected all with small children at home, the Mishna rules that a potty that has a leak such that liquids would escape, but not excreta, retains its status as a kli.
In addition to laws of purity, one can learn from the above mishnayot that while multi-purpose vessels were apparently rare, bathhouses were common, something to be expected before the invention of modern plumbing.
Other issues discussed in the first part of the chapter include the size a hole needs to be if the vessel itself is smaller than a pomegranate, and the size of a pomegranate itself, which the Mishna teaches, “is neither a small one or a big one but a medium-sized one”.
While frustrating to us moderns, a pomegranate was a most acceptable measurement in ancient times, when exactitude was not even a goal (perhaps because it was unattainable). Thus, the chapter continues that those items that required a k’beitzah, the size of an egg—for example, the size of food needed to become tameh—required an average-sized egg. Ditto for those areas of halacha that require a k’zayit, the size of an olive, i.e. eating matzah, it the size of an average olive that we must eat. But we need not eat matzah the actual size of a zayit, an olive; rather, we must eat a k’zayit, the amount of matzah that is "like an olive" i.e. is more or less with the size of an (average) olive.
While the bulk of the masechet deals with technicalities, technicalities that were of great practical significance, at least two mishnayot of the masechet should be of interest to many and are oft-quoted to this day.
“If one cut the [impure] oven up into rings, and then put sand between each pair of rings, Rabbi Eliezer says: It is now pure. But the Sages say: It is tameh” (Kelim 5:10). Rabbi Eliezer and the Sages debated whether a broken oven put back together with sand linking the various parts instead of clay is considered to have the status of an oven. Rabbi Eliezer argues it does not, as such is no more than a piecemeal, temporary oven. This obscure debate would be unknown to most if not for the concluding line of the Mishna. “This is the oven of Akhnai”, the debate over which literally shook the rabbinic world and led to the excommunication of Rabbi Eliezer, the death of Rabban Gamliel and the assertion that rabbinic interpretation of text carries more validity than the interpretation given by a heavenly voice, i.e., a prophet (see Bava Metzia 59b and see here and here for some thoughts on this powerful oven).
A second Mishna (this one in the first chapter, and one that caused little debate) teaches that, “There are ten [levels of] holiness: The land of Israel has greater sanctity than all other lands. And what is [the nature of] its holiness? That the omer, bikkurim and shtei halechem, two loaves of bread, are brought from it, which cannot be done from other lands”.
The Mishna then lists the increasing degrees of sanctity starting from walled cities—where no dead bodies, once removed, could return—to the various areas of the Temple culminating in the “Holy of Holies”, where none could enter save for the kohen gadol on Yom Kippur in the time of his service.
Why this Mishna appears in masechet Kelim, of all places, can be explained by noting the prior Mishna, which discusses the “ten types of impurity that emanate from a person”. In editing the Mishna, Rebbe Yehuda Hanassi wanted to teach that the opposite of tumah is not tahara, but rather kedusha. Tahara is the absence of tumah, but kedusha is much more. If tumah means contact with death, kedusha means celebrating life. If there are ten aspects to tumah, then there must be ten levels of kedusha. If tumah means we are distant from G-d, unable to enter the Temple grounds, kedusha reaches its apex when the kohen gadol, the representative of the people, has a private encounter with G-d in the Holy of Holies.
 Bava Kamma, Bava Metziah and Bava Batra, the three opening masechtot of seder Nezikin, were at one time one long masechet, actually called masechet Nezikin, consisting of 30 chapters and 266 mishnayot. However, due to its length, it was eventually divided into its three current masechtot. I hope I am not out of line by suggesting that because masechet Kelim is somewhat less popular than the “three Bavas”, and because there is no associated Talmudic text, that little need was felt to divide it into smaller sections. Ironically, one often does see this division when people are (often desperately) trying to find people to learn masechet Kelim for a sheloshim.
 This is totally separate from the discussion as to whether our olives today are smaller than during the time of the Mishna. Even it such were to be the case—something that is very unlikely—there would still be no need for exact measurements. Eating something more or less the size of an olive is considered eating, regardless of what the size of that olive might be.
 Why the Mishna lists these three specific mitzvot to demonstrate the holiness of the land is not readily apparent. The omer and shtei halechem were brought as a communal korban such that very few ever saw it brought, and while bikkurim were brought by all farmers, even the smallest of amounts fulfilled the mitzvah. Why not list trumot and maaserot, or shmitta, which had a much greater relevance to the average person? Perhaps we can suggest that it is because these—the omer, shtei halechem and bikkurim—all had to be brought to the Temple, the centre of sanctity in Jewish life.