All mid-latitude lows form and develop along a zone of relatively large horizontal temperature contrasts. As a classic example, consider the surface temperature and pressure fields in the very early stages of the "Blizzard of 1993" at 12Z on March 12, 1993.
Clearly, the 500-mb short-wave trough, which provides upper-level divergence, acts like a match, sparking the initial flame of cyclogenesis. Given this spark at 500 mb, what feature serves as the fuel that enables the flame of cyclogenesis to burn brighter and more intensely? The most obvious candidate is the frontal zone and its relatively large horizontal gradients in temperature.
The $64,000 question now becomes "How do temperature contrasts associated with a front serve as fuel for a developing low pressure system?". The explanation is crucial to your fundamental understanding of weather forecasting. So I will spare no details.
Let's start over with a simple, west-to-east stationary front and suppose a 500-mb short-wave trough and its associated "vort max" approach from the west. In turn, upper-level mass divergence on the eastern flank of the shortwave trough causes surface pressures to fall, with a center of low pressure forming underneath the area of maximum divergence. In an effort to erase the loss of mass in the column of air over the low (the atmosphere runs a tidy ship), air converges toward the center of lowest pressure. In the process, cold air starts moving southeastward. A cold front marks its leading edge, with cold-air advection following in its wake. Meanwhile, cold air east of the fledgling low starts to retreat, allowing warm air to advance northward. A warm front marks its leading edge, with warm-air advection occurring north of the warm front.
By the way, cold and warm fronts can never (repeat never) originate from the center of a high pressure system. Remember that a high marks the homogeneous core of an air mass, so there are no large temperature and moisture contrasts at and around the center of a high pressure system. Any apprentice forecaster caught drawing fronts from the center of a high will be demoted (just kidding, but I caution you that drawing fronts from the center of a high will cost you big time on the promotion quiz).
This couplet of cold and warm advection associated with the fledgling low becomes the fuel by which the flame of cyclogenesis starts to burn brighter. To see what I mean, I'll first focus on the impact of cold-air advection west of the center of the low. For starters, I point out that the area of cold-air advection extends from just east of the center of the surface high pressure system following on the heels of the developing low to the cold front (in this region, winds typically blow from the north or northwest). Thus, the 500-mb short-wave trough lies over the region of cold advection.
Now please focus on the column of air underneath the core of the 500-mb short-wave trough (the coldest column, on average, from the ground to 500 mb). For all practical purposes, the brunt of the cold-air advection into an air column in the wake a cold front takes place between the surface and 850 mb. With colder air having entered the column from the north or northwest, pressure now decreases faster with height above the ground. In effect, the 500-mb height of the air column "falls" (in other words, the 500-mb height decreases). As 500-mb heights lower in other air columns in and near the center of the trough (also in response to cold-air advection), the short-wave becomes more sharply curved. In turn, positive relative vorticity increases as cyclonic curvature sharpens. Thus, absolute vorticity also increases in the strengthening 500-mb trough. In short, the "vort max" becomes larger (animation).
A more powerful "vort max" means that the mass divergence to the east of the 500-mb trough also gets larger and, as a result, the low intensifies as the surface pressure decreases at its center (assuming, of course, that there is net mass divergence in the air column over the low's center; in other words, upper-air divergence exceeds mass convergence in the lower troposphere).
Now the stage is set for a positive feedback process akin to the zinnias growing and blooming in my garden. With the surface low now "deeper" (a lower pressure reading at its center), the system's counterclockwise circulation of air increases -- both in scope and vigor. Indeed, strengthening winds circulating around the low extend their reach farther north (and south), drawing increasingly cold air southward (and warm air northward). In turn, cold-air advection becomes more intense in response to increasing temperature gradients. Enhanced cold advection then causes 500-mb heights to lower and the 500-mb short-wave trough to intensify and sharpen. The 500-mb vort max increases, leading to greater mass divergence east of the trough, which, in turn, causes the surface low to deepen. And so on and so forth. Meteorologists call this positive-feedback loop self-development because a mid-latitude low generates it own cold-air advection, which, in turn, causes the system to intensity.
To add a realistic flavor to this discussion, we will look at two stages in the development of the "Blizzard of 1993". In the figure below, the top row of maps corresponds to 12Z on March 13. On the left, note the 500-mb height analysis. If you drag your mouse over this chart, the corresponding pattern of 500-mb absolute vorticity will appear (note the "vort max" over the Gulf of Mexico). On the right is the surface analysis. If you move your mouse over the surface analysis, you'll see the field of temperature advection at 50 meters above the surface orchestrated by the low. West of the low, the magnitude of cold-air advection is greater than 2.5 degrees Celsius per hour, which translates to about 4.5 degrees per hour. Recall that such a rate means that cold-air advection, acting alone, would lower the temperature to the tune of about 4.5 degrees per hour, assuming that it persisted and that were no other heating or cooling sources that could also influence local thermometers (usually there are such sources).
At any rate (no pun intended), the cold-air advection behind the surface low apparently fed back to the 500-mb short-wave trough in positive fashion, causing the trough to markedly intensify by 00Z on March 14 (note the "22" vort max over the Carolinas). About this time, the surface low entered the stage of occlusion.