In guitar technique, alternate picking is when you have hammer-ons and pull-offs whenever you change frets on the same string. You will only pick a string when you move to another one. In essence, you will pick alternately every couple of notes.

In guitar technique, alternate picking is the alternating use of upstrokes and downstrokes. Comes in very handy when playing lines that bounce back and forth between strings (eg, the exercise The Spider), or playing lines that have an even number of notes per string (for lines with an odd number of notes per string, economy picking is much more useful. Not to be confused with slurring.