The number of years of unbroken service that a member of a standing Congressional committee has on that committee. The Rules of the House and Senate (and the rules of the Democratic and Republican caucusses within each chamber) have always given great weight to differences in seniority in allocating power and privileges among their members. The majority party committee member with the most seniority will almost invariably be selected as chairman of the committee and thus be awarded the power to hire and fire most of the committee's staff employees, to set meeting times, to determine which majority party members will be appointed to which subcommittees, to control what bills will be taken up for consideration, and so on. The minority party member of the committee with most seniority is designated the ranking minority member of the committee and thus gets to pick the minority party members of subcommittees, hire and fire the minority's (much smaller) share of the committee staffers, and generally act as his party's main spokesperson on committee matters to the chairman, as well as the mass media, etc. When bills drafted in the committee are reported out for debate by the whole House or the whole Senate, the Chairman and the ranking minority member get to decide which members of their party will be recognized to speak in the debate, and for how many minutes. All the other members of the committee are ranked according to their years of membership, and such matters as the order in which they get to speak during committee meetings or hearings, chairmanships of subcommittees and many other privileges are normally determined largely or entirely on the basis of their seniority within their party's ranks.
Since a Representative's or a Senator's degree of power and influence over the content of the legislation produced by the committee are very largely determined by seniority, and since they have to start all over in accumulating seniority if they change committee assignments, members of the US Congress normally wish to stay on the same committees year after year -- at least after the first few years in office. (A member or two may have to be booted out of his committee assignment involuntarily if the latest election results resulted in a sizable shift in the party balance within the chamber as a whole, resulting in the losing party losing some of its slots on all the committees. But if that happens, it is the least senior member of the losing party on the committee that has to give up his membership.)
Following the principle of seniority creates a well-established "pecking order" within the Congressional committees and the party caucusses and thus probably helps to avoid a lot of acrimonious conflict over perks and status that might otherwise make it harder for committee members to work together on more substantive legislative issues. The premium placed on seniority probably also tends to ensure that committee members (or at least the most influential ones of them) develop an enormous amount of expertise and detailed knowledge about the policy issues and the administrative problems connected with them in the area of policy supervised by the particular committee. On the negative side, the seniority rule gives disproportionate power to Congressmen and Senators from "safe" districts and thus tends to minimize the impact of shifts in the voters' choices, since pretty much the same old players will still be dominating the committee's deliberations after the election as before almost regardless of the outcome.