What does a second dot placed after a musical note or rest mean and what does the first dot mean?

In musical notation, a second dot placed after a note or rest indicates that the beat is to be extended by one-half of the value of the first dot. The value of the first dot depends on what the original note is.

The double-dotted note always increases the length that the note is played or the time of the rest. Here's one example: when you begin with a quarter note (played for one beat), and then place a dot after that note, that extends the note's duration to 1.5 beats. Adding a second dot would then draw the note out to 1.75 beats.