Last year's Tu B'Shevat post is here, with links to earlier posts. Plus there is this post from earlier this week.
For biblical background, see here. The name "New Year for Trees" comes from Mishnah Rosh HaShanah 1.1. That passage gives two alternative dates for the celebration, one from Shammai and one from Hillel. Hillel's date (15 Shevat) is the one celebrated at present.
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