When mirrorless cameras first became available, the way in which they autofocused was essentially in the same way as a compact camera, a system known as contrast-detect AF. This uses the main image sensor to measure the point at which contrast is highest as a lens moves through its focusing range, and as this is the same sensor that ends up capturing the image, the method is very precise: what you see is what you get.
The downside, however, is that on many cameras it’s quite slow. Compact cameras have much smaller lenses with lighter internal elements, and these can move efficiently when focusing. Lenses designed for mirrorless cameras are typically larger and heavier, and this system cannot measure contrast quickly enough to make it useful against a moving subject. If you ever used live view on one of the first generations of DSLRs to offer this feature, you may already appreciate just how slow this could be.
DSLRs focus using a different method as standard, a system known as phase-detect AF. This is typically much faster than contrast-detect AF but there is potential for it to be less accurate, as the focusing sensor used to do this is separate from the main image sensor (the more basic design of a mirrorless camera prevents them from making use of this separate focusing sensor). The solution? To combine the two principles on the main sensor, the one used to capture the image.
By maintaining contrast-detect AF while using with pixels on the main image sensor that could perform phase-detect AF, you essentially got the best of both worlds. This kind of setup is not only now found on mirrorless cameras, but on compacts and DSLRs too, and it’s (usually) this that the manufacturer refers to when they speak of ‘Hybrid’ AF systems.
So what does this mean for mirrorless cameras? It means the gap in focusing performance between DSLRs and mirrorless has significantly narrowed in recent years, to the point where some mirrorless models can focus alarmingly quickly. DSLRs have also benefitted from this technology, however, not only to provide faster focusing when using live view but also to allow for smooth focus transitions and tracking during video recording.
Of course, focusing is only one part of what makes a camera suitable for a particularly type of photography, and many sports photographers continue to use DSLRs rather than mirrorless cameras. Even so, the ability of a focusing system to do what you need it to is a critical feature for the action photographer, and many mirrorless models can now be successfully used for this kind of photography where they would have previously been completely unsuitable.