Trust flow and citation flow are metrics designed by Majestic - a backlink measurement tool that many SEOs use. Other backlink tools have different names and measure links in different ways. The two measures together can paint a picture on how balanced a sites backlinks are, often illuminating sites that obtained links in a spammy or manipulated, non-trustworthy way.
Citation flow is Majestic's attempt to measure Google's PageRank data, which is a combination of quantity and authority of links. For majestic, this is a logarithmic scale from 0 to 100. Links from sites with more backlinks count more than links from sites with no backlinks.
Trustflow is Majestic's attempt to measure Google's TrustRank data. To determine how trustworthy a site is (in an attempt to weed out spam and heavily manipulated backlink profiles), search engines created a human edited list of seed sites they deem highly trustworthy (including wikipedia, news publications, libraries, etc.). Trust could be determined by how far away a particular site is from being linked by the seed set of trusted sites. For Majestic, the scale is 0 - 100. A site near 100 would have direct links from the trusted sites (or be one of the trusted sites) and links from other sites with high trust values, while a site near zero would have no link connection to the trusted sites, even through many layers of backlinks.
When you plot the two measures together you get a Trust Ratio. If the graph tilts too far towards the citation site, without the trust ratio to support it, then the site may be deemed less valuable to search results then its backlink profile might suggest. An example of this would be a spammy site that has links from many sites, even ones with decent PageRank, but is never in the neighborhood of trustworthy sites and thus could be penalized with lower rankings despite what looks like an authoritative site off pure backlink counts.