What does high thyroid peroxidase mean?

Depends. If you mean antibodies to thyroid peroxidase, it may suggest auto-immune thyroid disorder.
Thyroid antibodies. The presence of anti-thyroid peroxidase antibodies signals the presences of autoimmune thyroid disease. This is often, but not always, associated with underactivity of the thyroid. The change in level of the antibodies does not have any real significance; what is important is that your dose of thyroid hormone replacement results in your having a normal TSH level.