There are three main reasons to learn Biblical Hebrew:
1) Experiencing the Unknown
Hebrew belongs to the Semitic family of languages, whereas English (and Spanish, German, Latin, etc.) belong to the Indo-European family. However, all language still seeks to attain the same goal (that is, communication) and end up using the same kinds of forms (nouns, adverbs, prepositions, etc.) – therefore, studying Hebrew is an excellent way to study linguistics in a way far different than our own and yet oddly similar.
2) Reading the Old Testament
Hebrew is best known for the Old Testament. Those persuaded of the Jewish or Christian faiths have a clear reason to desire to read their Scriptures in the original language – both to ascertain a closer understanding of the text and to guard against the errors of others. However, even secular persons or those of other faiths have reason to study the Old Testament as history or literature, and reading it in the original language can only serve to strengthen such endeavors.
3) The Better Reading of the New Testament
The New Testament is written in Koine Greek; however, it was written by authors (and filled with descriptions of persons) who were Hebraic in culture. As such, Biblical Greek is heavily influenced by the Hebrew language. Furthermore, the New Testament and Church fathers quote the Old Testament heavily (though typically using the Septuagint, a Greek translation thereof); learning Hebrew can therefore give very valuable insights into how early Christians used their Old Testament.