I was looking through some sheet music, when I noticed quite a few pieces had pickup notes. What is the use of a pickup note? Here is an image:
Pickup notes are just a symptom of the fact that many melodies don't start on one of the intuitive downbeats, but between two of them. If the notation bothers you, you can always rewrite such music by inserting a bunch of rests before the pickup note, so that the first bar is a complete bar.
Used quite often in songs where words need to make sense and fit into the rhythm. There is a tendency for an important word or first syllable of that word to be placed on perhaps the most important beat of a bar - beat one. If a word/syllable needs to precede that, it's going to be in the previous bar, as a pick up note - properly known as the anacrucis
'Happy Birthday' has one such anacrucis. The emphasis is more on Birthday than Happy, so happy is the pick up part, in the bar before the first full bar.
If you're concerned about it being alone in a bar 'What's the use of pick up notes?' is an odd question phrased that way; then generally speaking, the rest of that bar is usually found at the end of the verse, or song. If the anacrucis is crotchet long in 4/4, then the last bar will be 3 crotchets long. This keeps the rhythm going when looping the song, or singing the second verse.
It also happens in instrumentals, again where the composer decides that there will be something before the first 'main, important' note of the tune. I guess some of us use this sort of thing a lot when speaking - 'Erm,...'
What is the use of a pickup note?
This may sound glib, but I don't mean to...
Why ask that question alone, but not also "what is the use of a note on the beat?"
The point of both is to create the sense of meter.
In order to feel a meter something has to create an emphasis on beat one (or generally on strong beats.) By necessity whatever is not emphasizing the strong beats will have less emphasis.
From a metrical perspective the pick up note (anacrusis) is there to clarify the emphasis on a strong beat. This is closely connected to the sense of a barline and the beginning of phrases. So you can also say a pick up note can be used as a phrase beginning, a phrase articulation device.
From a performance perspective you probably want to articulate a pickup note to de-emphasize the note. A typical thing is to play it a bit lighter.