Ramp rate is literally the first step in the four-part reflow process and plays an important role in the formation of the intermetallics. Ramp rate, from room temperature to peak, needs to be watched for a few reasons. The ramp rate determines both the spread and volatization of the flux, and has a hand in voiding and oxidation build up.
A slow ramp tends to allow more solvent volatization, or "out gassing". Slow ramps for solder pastes are usually 0.75-1°C per second. (For reference, a "typical" reflow profile has a ramp rate of 1-2°C per second, which generally poses a balance between spread and out gassing.) This slow ramp keeps the flux close to where it's been applied, reducing spread and slump. This also gives enough time for the full volatization of the solvents in the flux, usually reducing voiding, as well as keeping the ΔT of the board well under 10°C. All this extra time may have a detrimental effect on some other points of interest, though, especially oxide build up of both the component and substrate metallizations, as well as the solder alloy itself.
On the flip side, a faster ramp reaches the softening temperature of the flux quicker, and therefore the flux (and paste) spread to cover a greater area, which increases the area of the joint. It may also allow for some of the activators to be saved for the actual liquidus of the alloy. Of course, there are downsides to this approach, which are the possibility of voiding (sometimes severe) and a high ΔT across the board.