Celery stalks have long 'strings' in them which many people find unpleasant. The strings can be wholly or partly removed before cooking - snap the bottom end of the celery and a small portion of the strings will be visible. Just grab them one at a time and pull firmly upwards and they'll come out. Thinly slicing celery crosswise is a less-wasteful way to deal with this annoyance.
The seeds are considered a spice.