A font consists of a number of glyphs. In order that the glyphs may be printed, there has to be some way of accessing them; in TeX they're arranged in a numerical order called an encoding, and their number in the encoding is used. For various reasons, Knuth chose rather eccentric encodings; in particular, he chose different encodings for different fonts.
When TeX version 3 arrived, some at least of the reasons for the eccentricity of Knuth's encodings went away, and at TUG's Cork meeting, an encoding for a set of 256 glyphs, for use in TeX text, was defined. The intention was that these glyphs should cover `most' European languages, in the sense of including all accented letters needed. (Knuth's CMR fonts missed things necessary for Icelandic, Polish and Sami, for example, but the Cork fonts have them.) LaTeX2e refers to the Cork encoding as T1, and provides the means to use fonts thus encoded to avoid problems with the interaction of accents and hyphenation (hyphenation of accented words).
The only METAFONT-fonts that conform to the Cork encoding are the EC fonts (available as fonts/ec. They look CM-like, and are now regarded as `stable' (in the same sense that the CM fonts are stable. Their serious disadvantage for the casual user is that they are large - each EC font is roughly twice the size of the corresponding CM font; what's more until corresponding fonts for mathematics are produced, the CM fonts must be retained.
The EC fonts supersede the experimental DC fonts, which have now been removed from the archives. They are distributed with a set of `Text Companion' (TC) fonts that provide glyphs for symbols commonly used in text. The TC fonts are encoded according to the LaTeX TS1 encoding, and are not viewed as `stable' in the same way as are the EC fonts are.
The Cork encoding is also implemented by the PSNFSS system, for PostScript fonts.