The first NPN transistor acts as the reference. The second NPN transistor "mirrors" this current. In this way, the currents in the strings are automatically equally shared. The 1Ω emitter resistors are not strictly required for the current mirror to function, but in practice they help compensate for differences in Vbe between the transistors and improve current balance accuracy.
A current mirror also provides protection against LED failures. If any LED in the first string fails open circuit, the second string is protected (since the reference current drops to zero, the current in the other strings also falls to zero). Likewise, if any LED fails short circuit, the currents remain equally balanced.
However, if an LED fails open circuit in the second string, the current mirror does not protect the LEDs in the first string from being overdriven. A modified version of the circuit can prevent this, using a dummy load with the first transistor to set the current in the remaining strings. It is also possible to extend the current mirror to three or more strings by connecting additional transistors with their base connections paralleled.
Some LED driver manufacturers claim that LEDs inherently share current equally, making external current mirror circuits unnecessary. This is not always true. An imbalance will exist unless the combined forward voltages of the LED strings are exactly the same.
If, for example, two parallel strings are mounted on a common heat sink, the string drawing more current will run brighter and hotter. As the heat sink warms up, the Vf of the second string drops, causing it to draw more current in turn. In theory, this thermal feedback should help balance the currents, and in practice the effect can be observed — though it is not reliable enough to ensure accurate current sharing.
Furthermore, if the two strings are part of separate LED lamps, there is no thermal compensation between them. The lamp with the lowest combined Vf will draw the most current, run hotter, and experience further Vf reduction. This positive feedback loop can worsen the imbalance and may lead to thermal runaway and eventual LED failure. Today, current mirror solutions are rarely used. The cost of accurate LED drivers has dropped so far that, for high-grade lighting, it is better to drive each string with its own current controller. In low-grade lighting, some imbalance and the resulting shortened lifespan are generally accepted as cost trade-offs.