Shower drains getting blocked with long hairs, which then knot-up in the pipe and eventually slow down the water drainage rate to a trickle, is a common problem. This is especially so with narrow-bore or older drains.
This simple but brilliant OXO `good grips' device is very well thought out. It's big enough to cover the entire drain aperture of almost any shower and has a rubber seal-ring around its circumference which performs two functions: it stays where it is and cannot be easily dislodged from the drain aperture by water pressure from the shower head, or by your feet, and it prevents the ingress of hair or any other matter under the edge. It has small drain-holes (it actually looks like a shower-head) rather than a mesh so is very effective at catching everything.
A minority of reviewers here report that it did not work well for them, with their particular shower drains. It's probably a good idea to consider their experiences too prior to purchase; it seems in most of these reported cases the surface containing the drain aperture was not flat, and therefore because this OXO device is larger than most in diameter, it won't work with a curved tub. I can only re-state that in our shower (which has a flat floor), it works brilliantly and I can't think of how it might be improved.
Overall, this is an intelligently designed product where all the small details have been thought through and addressed. Highly recommended for the job, and cheap too.