Answer: A major triad is a perfect fifth combined with a major third (4 halfsteps) above the lowest note. Example: C-E-G.

A minor triad is the same but the third is minor (3 halfsteps). Example: C-Eb-G.

Rearranging the notes doesn't change their basic nature: E-G-C is still a major triad but it's "inverted." Most of the music we listen to is basically major and minor triads in succession with various added tones like sevenths, plus decorations and connecting tones.

Either kind of triad could be found in both major and minor keys. In the key of A minor the chord built on the tonic note A is a minor triad (A-C-E), while the chord built on the third note of the scale is major (C-E-G). In the key of C major it's the major triad C-E-G that is built on the tonic note, while the triad built on the 6th note is minor (A-C-E).

When you hear a piece in A minor you hear music that centers on the A minor triad and probably makes use of the chords, A minor, D minor, E major... when you hear music in C major you're hearing music centered on C, with the main chords being C major, G major, D minor, F major... You won't hear very much music that uses only major or only minor chords, fortunately, though a short and simple major piece in C might get by with just C major, F major, and G major.

So, major triads are different from minor ones, but both are used in major keys, and both are used in minor keys. You can't get very far without having both.