Japanese for "I don't know" or "I don't understand". The standard polite negative conjugation of the verb wakaru, "to understand".
Nonnative speakers are often confused between wakaru and a verb of similar meaning: shiru, "to know". One might be tempted to use shirimasen instead of wakarimasen, especially when asked a question to which one doesn't know the answer. However, in Japanese, shiru tends to have the connotation "I don't know, and I don't care". (You might think of it as similar to replying, "As if I would know.") Hence it may come across as odd--such as if someone asked you where you are--or downright rude.
One exception is when you speak of knowing a tangible thing, especially a person. In that case, one would use shiru and it would sound strange to use wakaru. (Thank you eliserh for reminding me.)