I'll give you the quick & dirty version:
The balance ratio of a mechanical seal is an area ratio and is related to the seal face load. Balance ratio is defined as the ratio of the closing area to the opening area. Seals with a balance ratio > 1 are 'unbalanced'; ratios of < 1 are considered 'balanced'. Seals are balanced to decrease friction and wear, so you will usually move to a balanced seal at pressures of 250 psid and above (although you can use them at lower pressures as well). Unbalanced seals will be used up to 250 psid. The theory becomes more complex when you talk about metal bellows style mechanical seals; in those designs the balance ratio will increase at higher pressures primarily due to the bellows plate geometry. Visually if you were to look at the primary face of an unbalanced pusher style seal vs. a balanced pusher style seal you would notice a 'step' in the face geometry (reducing the closing area and changing the balance ratio).
In theory, the lower the balance ratio, the lower the fluid film temperature, the longer the seal life. In practice, leakage control can sometimes be sacrificed and the faces may become unstable depending on if the fluid is volatile (vaporizing), or if any other face distortions occur. In general, review of the application with your seal vendor is always recommended. If you are adhering to API 682; then balanced seals are your only options due to the nature of the services. The attached is a very rough representation of what I just said. It depicts a single set of seal faces pressurized from the OD: the balance ratio calculations will become more complicated when you discuss OD vs. ID pressurizations particularly in dual pressurized seals. Hope this helps.