Walking away from something and letting it "marinade" is a learning technique known as incubation. When conscious, incubation occurs in the sub-conscious mind where your brain will continue to essentially run series of diagnostic tests addressing the problem it has been presented with. When sleeping, incubation occurs in the unconscious mind, and some people might even have a dream about the problem they are dealing with.
This has been shown in mice wherein a given mouse was presented with a complicated maze. When sleeping, electrodes attached to the mouse's brain illustrated the mouse running through the maze over and over, assimilated learned information. The next day, the mouse was able to make it through the maze with little problem.
Incubation also has the added benefit allowing the person to approach the problem with a fresh perspective.
Typically, extended breaks from an instrument are not encouraged as a musician could lose a lot of fine motor-control and stamina. That said, extended breaks can be beneficial. For example, they could give a musician ample time to forget their bad playing / practice habits as well as renewing their enthusiasm and vigor for playing.
Small breaks (a few hours) are good and should be done often when practicing. Long, extended breaks (a week or more) should not be done frequently at all and in fact used sparingly.
N.B. Mentally practicing is also quite beneficial. If taking a break from your instrument, taking a practice session to mentally rehearse your music can aide in your practice as well.