January: 睦月 (Mutsuki) – Month of harmony
February: 如月 (Kisaragi) – Month of wearing more clothes
March: 弥生 (Yayoi) – Month of new growth
April: 卯月 (Uzuki) – Month of deutzia (a type of flowering plant)
May: 皐月 (Satsuki) – Month of planting rice
June: 水無月 (Minazuki) – Month of no water (ironic, as it's the rainy season)
July: 文月 (Fumizuki) – Month of letters
August: 葉月 (Hazuki) – Month of leaves
September: 長月 (Nagatsuki) – Month of long nights
October: 神無月 (Kannazuki or Kaminazuki) – Month of no gods (gods are believed to gather elsewhere)
November: 霜月 (Shimotsuki) – Month of frost
December: 師走 (Shiwasu) – Month of priests running (busy month)
I want to clarify, these were the traditional names of the months.