I once asked my Jyotish guru, K.N. Rao, if it's necessary to understand the meaning of mantras in order to get their benefit. His response was, "Mantras are medicine. I don't need to know the ingredients of my medicines for them to work." When I thought about this it made sense. If it's true that all languages emit a vibration, and Sanskrit is a spiritual language, then we can benefit by the vibration of mantras without knowing their meaning. It's like when you hear beautiful music sung in another language, like at an Italian opera, and you feel uplifted regardless of knowing the language. Sanskrit mantras are the same way, only more powerfully, because the language was developed for purpose of spiritual transformation.
The flip side to this question, is that Rao also often says, "What's important is to do your practices sincerely with devotion." For me, when I understand its meaning at least to some extent, I can recite a mantra with more devotion. For instance, I often recite the Vishnu Sahasranam, the thousands names of Vishnu, and the first name is "Vishvam" meaning, "the All." Just remembering this helps me get into a devotional state of mind as I start out. It may not be necessary to know this to get the full benefit, but I notice I do benefit by knowing the meaning also.
Read an article about the use of the Vishnu Sahasranam as a remedial measure for planetary afflictions by clicking here.