If I have understood correctly, in time a single qubit in superposition will collapse on it's own to the $|0\rangle$ or $|1\rangle$ state, but I thought it only collapsed when measured. How is the collapse explained if there isn't any measurement?
When we measure a qubit in superposition, we interact with the system, causing it to collapse into either $|0\rangle$ or $|1\rangle$, with certain probabilities determined by the coefficients in the superposition.
If a qubit were perfectly isolated, it would remain in a superposition indefinitely (or until a measurement, but then it wouldn't be isolated anymore!). However, qubits interact and become entangled (as per @EvgeniyZh) with their environment, which can cause a collapse of superposition and the transition to classical behavior (which is very well explained here). This is decoherence. Decoherence is an issue in quantum computing because, if a qubit becomes entangled with the environment and decoheres, we can’t undo the damage to the qubit if we don’t have full knowledge of the environment in which it was entangled with (which we don't).
So in essence, decoherence leads to the leakage of quantum information into the surrounding environment, and since we lack the ability to control this environment, the retrieval of this information becomes impossible.