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  The triad is a "stack" of three notes, it is the smallest stack of notes that can technically be called a chord.  Two-note "stacks" are called dyads but are often referred to as chords and that is not something to get hung up on. 

Triads are composed of three elements, a Root, from which the triad derives its name, a third, and a fifth.  (If you are new to this information please download the PDF below to accompany this description.)  They have these names because if you look at the piano and start on a note, in this case, C, skip over a note, which would be 2, and then land on the next note you will end up on 3.

We start with the Major Triad which is built by starting on a root note also called the tonic, in our example C and going up a Major 3rd (4 H.S.)  this is also called the root of the chord and a Minor 3rd (3 H.S) also called the 5th of the chord.   Sometimes these are called Major Minor chords.  

Next is the Minor Triad which is constructed from a root note (tonic) and a Minor 3rd and then a Major 3rd sometimes called a Minor, Major chord.  (Imagine that!)

Moving on is the less common Diminished Triad which is constructed of a Root, Minor 3rd and another minor third.  Sometimes called, you guessed it, a Minor Minor chord.

The least common triad is the Augmented Triad which consists of a Root, Major 3rd and Major 3rd.  (Yep, Major Major chord)

In their basic form, 7th chords are created by adding another note either a Major or Minor 3rd on top of a triad.  (See and download PDF below)

Before we go on a note (pun intended)  about nomenclature.  There is much confusion and sometimes conflict about how jazz or extended harmonies are notated.

Major 7 = Maj7 or the somewhat old-fashioned   Δ7

Minor 7 = Min7  or m7 or -7

Dominant 7 = (The dominant 7 is denoted by simply adding 7 to the Root  i.e. C7)

Half diminished = 7b5

Fully diminished = °7

It is also important to note that in most jazz charts the 7 designation implies higher extension i.e. 9, #11, 13...etc.