At the time when the Beth Hamiqdash (the Temple) stood, people who made vows in their mind only, without actually uttering the words with their mouths, were held responsible to carry those vows out.
Think about all those small and big promises which we make to ourselves but do not end up keeping. One classic example is: " Tomorrow I'll start a ... diet". It goes without saying that when we make any promises to others, even small children, we must be extremely careful to fulfill those promises.
Hakham Mordechai Eliyahu, 'a"h, (Dibre Mordechai, Parashath Mattoth), poses the following question: We may fully understand why one is obligated to fulfill vows when it concerns holy matters (pledges for synagogue, for example), and even to one's fellow Jew, but why are we particular about vows or promises one makes for oneself?
The answer is that our speech is holy. Rabbenu the Hida, 'a"h, amongst other Torah scholars, comments that our spoken words here, on this earth, make a remarkable impression in the upper worlds. He adds, that if one may wonder how such a thing is possible, the following example may illustrate it. He writes that when people step on grapes to extract their juice for the purpose of making wine, an unusual phenomena takes place. The wine kept in peoples' cellars starts moving! It may be hard for us to comprehend, for nowadays people do not keep wine in big barrels in their cellars, nevertheless, the message is clear: if the wine in the barrel is affected, we can understand that our actions on this earth have an affect in the upper world.
Our speech is holy and as such we must work on ourselves to perfect and sanctify our words and keep every single promise we make.