It's about the amount of noise (random/chaotic year-to-year variation) in the data, compared to the scale of the trend you're trying to measure. In the case of the longwave radiation graph jopo posted (the red line), the trend is very close to zero while the noise is very large. In the case of the surface temperature series, the trend is bigger relative to the noise, so the time period necessary to extract a statistically significant trend is shorter.
You can see this by comparing the top two graphs (top-of-atmosphere outgoing longwave radiation and surface temperature). As a very simple illustration, draw a horizontal line through each one at the average value of the set (just by eyeballing it is fine for this). For the red plot, you'll find approximately equal numbers of points above and below the line throughout the time series. For the blue plot, the majority of points below the line will be at the early time points, and the majority above the line will be at the later time points.
