Observance is when you obey a rule or law, or follow a long-standing tradition. If your religious observance requires you to fast for several days, you might ask your track coach to let you sit out a race.
Observance of traffic laws will usually keep you from getting expensive speeding tickets. And, practicing a religion usually includes various kinds of observance, from attending church or temple to wearing certain items of clothing. You can also use this noun to mean "watching or noticing," like a bird watcher's careful observance of a bush where he once spotted a rare finch — although this is more commonly called observation.