Type Ia supernovae (SNe Ia) have been proposed to be much better distance indicators at near-infrared (NIR) compared to optical wavelengths - the effect of dust extinction is expected to be lower and it has been shown that SNe Ia behave more like `standard candles' at NIR wavelengths. To better understand the physical processes behind this increased uniformity, we have studied the Y, J and H-filter light curves of 91 SNe Ia from the literature. We show that the phases and luminosities of the first maximum in the NIR light curves are extremely uniform for our sample. The phase of the second maximum, the late-phase NIR luminosity and the optical light-curve shape are found to be strongly correlated, in particular more luminous SNe Ia reach the second maximum in the NIR filters at a later phase compared to fainter objects. We also find a strong correlation between the phase of the second maximum and the epoch at which the SN enters the Lira law phase in its optical colour curve (epochs ~15 to 30d after B-band maximum). The decline rate after the second maximum is very uniform in all NIR filters. We suggest that these observational parameters are linked to the nickel and iron mass in the explosion, providing evidence that the amount of nickel synthesized in the explosion is the dominating factor shaping the optical and NIR appearance of SNe Ia.