A suite is a collection of pieces related by a central theme or idea. Suites can be a collection of songs that deal with a specific topic such as Gustav Holst's "The Planets." Each movement deals with a different planet and tries to create a musical depiction of astrological elements related to the respective planet. Suites are generally more programmatic in nature and deal with specific story lines and events.
Fugues are a remnant from the Baroque period of music. The composer creates a main idea and then plays with the idea throughout the piece. In a fugue, the main idea repeats at a higher interval and then breaks up into smaller musical ideas. The piece then goes through a transition, a development section in which the music goes through several keys and then finally, a return to the initial idea.
A sonata is similar to a symphony, but it doesn't require unifying themes throughout the piece to hold the work together. In a sonata, there are typically four movements, although three movement sonatas are also common. Each movement has a related key and may deal with different musical subjects. A form commonly mistaken with the sonata is the sonata-allegro form in which the piece has several parts, including an exposition, development and recapitulation.
A concerto is a musical work played with an orchestra and a soloist. Traditionally, the soloist played with an orchestra to qualify as a concerto but in modern music, that distinction has somewhat faded. There are now concertos that use the piano instead of the orchestra; however, the basic concept of a concerto involves the use of a solo instrument and some sort of background ensemble.