Euthymia in a bipolar disorder is simply defined as a relatively stable mood state, neither manic/hypomanic nor depressed. However, some dictionary definitions have shades of meaning that might be confusing in the context of the usage of the term bipolar disorder and similar mental illnesses. To further complicate things, a significant number of euthymic bipolar patients still show some traits of depression.
The confusion in basic definition begins with the root word of euthymia. In Greek, the root word means "gladness, serenity, good mood." This leads to definitions like "a pleasant state of mind," and "joyfulness; mental peace and tranquility."
However, in terms of bipolar disorder, such words as "pleasant" and "joyful" can't be an essential part of the definition. A euthymic mood may be pleasant but does not have to be.
In clinical terms, a euthymic mood is one that rates low on scales of both manic and depressive symptoms. However, studies show that often some depressive symptoms do appear during euthymia, notably anhedonia (relating to lowered pleasure) and general cognitive impairment (such as memory problems).
Thompson, JM, et al. Neurocognitive impairment in euthymic patients with bipolar affective disorder. British Journal of Psychiatry. (2005) 186: 32-40
Dubovsky, Steven. Euthymia: It Depends on How You Define It. Journal Watch Psychiatry. 18 Aug 2008.
Mann-Robel, MC, et al. Meta-analysis of neuropsychological functioning in euthymic bipolar disorder: an update and investigation of moderator variables. Bipolar Disorders. June 2011, 13:4-334-342.