For general questions about chords like how to play them, construct them, or what symbols represent them. For more in depth analysis of the ideas behind chords themselves, please use the chord-theory tag.
See also harmony, which is more general and covers notes being sounded together with different relationships, and the way those relationships change over the course of a piece.
A chord is a musical structure containing multiple different notes that can be considered to form one harmonic entity at a moment in time. In Western Music Theory systems, chords are often considered to be the smallest building-block unit of harmony. The many different types of chords are often referred to as chord qualities.
Chords in a Western context are typically interpreted as "stacks" of major and minor thirds chained upwards from a single root note. Because of this, the name of a chord largely depends on the unique pattern of thirds beginning from the root note. The basic naming scheme also reflects this.
For example, a "major" chord comprises, from bottom to top, a major third followed by a minor third. "C Major" consists of C (the root), E (a major third above C), and G (a minor third above E). Similarly, a "C minor" chord is built from C (the root), E-flat (a minor third above C), and G (a major third above E-flat. All "major" and "minor" chords, and others, follow these same thirds-based patterns.
In practice, not all chords will be played in the exact same order from which they are commonly constructed. The rule of octave equivalency is observed within the structure of chords. While [CEG] is the simple "stack-of-thirds" order for the notes of a C major chord to appear, any of the three notes could be positioned in any octave, doubled or repeated several times, played by multiple different instruments, or even appear in any arbitrary order without changing the identity of the overall chord. The specific orders of the notes of a chord can be understood as chord-voicings, or simply voicings.
Often, a chord will be voiced with its root note as the bass note (lowest note found within the chord voicing). For effect, however, sometimes a chord will appear with one of its other notes as its bass note. When this happens, the chord is considered to be inverted. chord-inversions get their distinct properties as a result of the fact that in many types of music, the lowest-pitched parts of the music serve a unique role as a type of special countermelodic line that interacts strongly with the harmony above.
There are other methods of building chords: for example, "quartal", where chords are built in fourths; and "quintal", where chords are built in fifths. The types of chords constructed as a chain of thirds, accordingly, are often described as tertian harmony or tertian chords.