The fundamental dilemma for string players is that they don't hold the bow in the middle; they hold it at the end. That means that at one end of the bow, it's much easier to play loud than at the other.
This dilemma is one that has faced all string players going right back to the Stone Age, and the job of expressive artists is to try and counter that effect.
If you don't try to counteract the weight of the arm, the natural tendency is that the weight of the arm governs the sound that the bow creates; that is, the sound is allowed to diminuendo (get quieter) as the bow gets further away, and as the weight of the arm gets further away from the centre of the body. This also works in reverse, so on an up bow the sound crescendos (gets louder) as the weight of the arm gets closer to the body. To counteract this natural tendency players practise ancient excercises, playing the reverse of the effect above which can help to develop a constant controlled sound.
This fundamental dilemma of holding the bow at one end gives us what in the 18 century was called "The rule of the down bow". This meant that all of the musical stresses had to come on the down bow and all of the weak notes, on the up bow. But this was a rule that was there to be broken - rather like a dancer, gravity exists, but by acknowledging and challenging this rule the dancer can appear to defy gravity.
David demonstrates the 2nd subject of the 1st Movement, Dvorak cello concerto in the film, and above is the example written out. The anacrusis (up-beat of the phrase) starts on an up bow, so that the main note arrives on a down bow. The bowing works out very well from that point with down bows on the first beat of each bar, but reaches a problem in the penultimate bar above. The E natural dotted minum is both the end of the first phrase, and the transtion into the next phrase (which we haven't printed) and thus needs to crecendo (get louder), despite being on a down bow. David has to use both the bow technique and vibrato to move seamlessly into the next phrase. Fighting against the law of gravity, to crescendo on an up bow and by using an intense vibrato, David manages to make the E Natural ‘turn the corner’ and move back up into the next phrase. You can read more about this in David's film on vibrato.
These two elements of vibrato and bow control come together as one single expressive device that allows musicians to steer the music in the way that they want, to give it the melodic expression that is necessary, and to provide the life and bounce and energy that they need.