In music, there are various terms used to indicate tempo changes, mood, articulation and special techniques for specific instruments. These terms come from a variety of languages, but most commonly are from Italian, English, German and French. Musicians learn these terms as they practice new pieces and look up what a particular term means. Many of the terms are very similar, with subtle differences between each term. Often, as in the case with "rit," these terms will appear abbreviated to save space.
A ritardando is a gradual slowing of the tempo. Rit. is the shorthand most often used in scores. When you see the abbreviation of the entire word ritardando, the composer is asking you to slow down gradually. Usually this occurs over the course of several measures in the piece. A similar term, rallentando, is very much like a ritardando except that with a rallentando the performer is expected to slow down more rapidly and it is implied that the player should decrescendo, which is a fancy word for getting quieter.
Ritardandos tell the performer to gradually slow down, but a musician must determine how much to slow down. Often, a ritardando comes right before a tempo change. In these cases, most musicians will slow down to meet the new tempo less abruptly. Imagine if the music was buzzing along and then suddenly and drastically changed tempo. This is exactly the sort of issue the ritardando solves.
Gustav Mahler was famous for his use of large, sweeping ritardandos. Particularly in his 1st and 2nd Symphonies, there is great use of this technique. He will often use it at the end of phrases and sections to create a dramatic lull in the performance. Performers also use ritardandos to help exaggerate a musical line. Often, a ritardando appears in preparation for a solo line or in the middle of a lyrical piece. Ritardandos commonly appear at the end of a composition.
The notation of a ritardando is standard. The term appears spelled out completely or indicated with its abbreviation in the affected section. The term will most often appear below the score, although it occurs above the score in vocal music and when it would conflict with other score items if placed below. Most commonly, a broken dotted line will appear connected to the ritardando. The dotted line indicates how long the ritardando should extend. When the broken dotted line stops, that is the point where the tempo should stabilize.