The x-axis on this graph is based on the DW-NOMINATE left-right scores of each member of each U.S. House of Representatives from 1865 to 2015. This uses a member's voting record to measure the direction and extremity of their political views, regardless of party affiliation.
If a member's score on this axis is known, it's possible to predict their vote on any given issue with high confidence, given no other information about the member. Members whose votes are typically left-aligned receive negative scores, while members whose votes are typically right-aligned receive positive scores.
(However, see The Thin Blue Line That Stays Strangely Horizontal, which questions the validity of DW-NOMINATE.)
The extra points on the chart represent members who were at one point elected as independents (members of marginal parties, or with no formal party affiliation). Their entire career is plotted, with lines connecting their seats in subsequent Congresses. Changes of color mark where a member changed party affiliation between congresses: independent, Democrat or Republican.
Where there are black dots on the left hand side, you can hover or click on a year for more information.
There's some background information on my blog. You may also be interested in this poster from xkcd, on the same subject.