Does any one know what dB stands for?
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities.
http://en.wikipedia.org/wiki/Decibel
A little research on your own doesn't hurt, you know.
Raising the dB level of an audio clip makes it louder and does not change any of its other properties (unless you try to increase the sound byte volume over 0dB, in which case you will induce digital distortion and/or digital clipping and/or aliasing). If the sound byte is noisy, when you raise the volume by 20dB (for example) the dialog and the noise both get louder.
The reason the volume is low with the Zoom H4 (and the H4n, the Tascam DR-100 and similar very inexpensive audio recorders) is that they are intentionally made that way; they are primarily marketed to musicians who as a matter of course work at much higher dB levels and routinely distort their recordings. The internal mics and mic pre-amp scheme are set up so that the unit can be placed in front of a band that wants to record a rehearsal, for instance. The drummer is going to pound as heard as he can, the bass player will play as loud as he can, the guitarist has no comprehension of the term "Turn it down!" and the singer will be screaming at the top of her lungs into a $150 PA system, all in someones living room. The way the unit is biased by the mic/pre-amp scheme plus the compressor/limiter means that they won't have to turn the unit down to capture an undistorted recording.
As an independent filmmaker you will be capturing dialog; 75% of the time will it be at normal speaking levels, 10% will be screaming and 15% will be whispering or soft speech. Only the screaming will come close to the dB levels the unit was designed to accommodate. The unit also has (in digital audio terms) a very high self-noise floor (hiss) that would go unnoticed by a musician, but becomes all too apparent to those capturing more subtle sounds.
Digital audio recorders like the Zoom H4n, the Tascam DR-100 and similar units are popular with the indie film crowd because they are cheap, not because they record production sound well.
As I mentioned, for $100 you got a nice deal. But as with all ultra-micro-budget acquisitions you are going to have to deal with the problems as well as the benefits. You can raise the dB level without affecting the quality of the sound either positively or negatively (unless you distort it as mentioned previously).
One more piece of info while we're at it... Always get the mic in as close to the source a possible.
The Inverse Square Law
In simple terms, this means that a sound twice as far away is only one-fourth as loud. A sound four times as far away is only one-sixteenth as loud. So a human voice that records with adequate volume two feet away is just one-sixteenth as effective at eight feet.