TSH is a pituitary hormone that is affected by many things. When it is high, as your wife's result, that is indicative of her having Hashimoto's Thyroiditis. With Hashi's the autoimmune system erroneously identifies the thyroid gland as foreign to the body and produces antibodies to attack and eventually destroy the gland. As this proceeds, the output of hormone from the thyroid gland is gradually diminished and the pituitary produces more TSH, in an attempt to stimulate additional production of thyroid hormone.
Beyond that, the fluctuation in TSH level means very little. A high level does not create any risk for your wife, it only indicates that she most likely has Hashi's, so she should be tested further. Specifically she should be tested for the biologically active thyroid hormones, Free T4 and Free T3, which are not the same as Total T4 and Total T3, so insist on the Frees. Also, to confirm Hashi's she should be tested for Thyroid Peroxidase antibodies (TPO ab), and if found negative, then also test for Thyroglobulin antobodies (TG ab). Hashi's will show as high levels of one or both types of antibodies.
I expect that from those tests she will be found to have Hashi's and will need to start on thyroid medication. An important consideration will be whether she is having symptoms typical of hypothyroidism. So please tell us about any symptoms she has.