Think back to elementary school music class. You might be able to recall learn about Ta's, Tee Tee Ta's and other such noises that didn't make a lot of sense at the time. What you were actually learning in essence was the basics of beats and notes in common 4/4 time music.
What is 4/4 Time
When you look at sheet music, especially in popular music, most of it is in what's known as common time or 4 beats per measure of music. If you could out 1, 2 ,3 and 4 in a steady manner that would be one measure of music. How quickly you count those beats doesn't matter because the beats speed is the tempo not the time.
Whole Notes
A whole note stretches an entire bar of music. So in our example there would be one note per four beats. In the example above I gave you if you held the same note for the count of four that would be a whole note. This is of course if we're in common 4/4 time the length of that whole note would change pending the number of beats per bar.
Half Notes
A half note is exactly one half of a whole note. So in one bar of music in common 4/4 time there would be two half notes each lasting two beats or half as long as the whole note.
Quarter Note
You've probably already guessed it but a quarter note is held for half the length of time as a half note or one quarter the length of time as a whole note. All of these beats related back to the whole note by dividing it up into smaller pieces. With quarter notes in common time each beat (1-2-3-4) would receive it's own note.
This is the basic outline of beats, and it keeps going as a whole note can be divided down further into eighth notes and sixteenth notes the same way we did with the half and quarter notes above.