The peak of any insulin means when it is strongest, or working the hardest. At this time, your pet's blood glucose levels will be at their lowest, or at their nadir. Once you know this time for your pet on a particular insulin, you know the ideal time for a peak blood test. (While regulating it's often helpful to frequently take a mini-curve, a set of three blood glucose level readings at shot times and peak.)
Generally, the longer acting an insulin is, the longer it takes to reach peak. So it would take insulins like Ultralente and PZI longer to peak than intermediate-acting ones like Lente and NPH or short-acting ones like R/neutral.
Peak times are also determined by an insulin's suspension. Even though Lente and NPH are in the intermediate-acting class, NPH, with its isophane suspension, peaks before Lente and its zinc suspension.
Looking at an insulin's time-activity profile will give you the average time it peaks. However, this is only an average--it varies from individual to individual because of absorption and other unique factors. In some cases, pets and people rapidly metabolize the insulin. This speeds the time activity profile up for the person or pet. The onset (average time after injection the insulin begins working), the peak and the time the insulin becomes inactive (leaves the system) are much sooner than the time activity profile indicates.
The only insulins "without a peak" are Lantus and Levemir, when working correctly for the pet or person. They are then often used as a basal insulin to provide a virtually "flat response", and with a bolus insulin at mealtimes to provide extra insulin action.