Let's look at two elements of triads that will help in analysis and understanding of function.
Roman Numerals: Lesson
The use of Roman numerals has gone on for centuries in music. The fact that they have an upper and lower case make them perfect for analysing music.
We use upper case roman numerals to indicate Major chords: I, IV, V
We use lowercase numerals to indicate minor chords: ii, iii, vi
Here is a chart which shows how triads naturally occur in major and minor keys:
Just like intervals, triads can be inverted. We do this to alter the sound of the triad and often to allow for a more interesting bass line.
Here is a chart which shows how inversions are annotated in musical analysis: