It's important to check your tyres regularly. I'm reminded of this when we have torrential summer rain. The minimum legal tread depth for a vehicle tyre is 1.6mm across the central 3/4 breadth of the tyre, and around the entire circumference.
You can check your tread depth easily by comparing the tread against the tread wear indicator which is embedded in the tyre groove. If the highest point of the tyre is at the same height as the tread wear indicator it's time to visit the tyre fitters.
Consider changing tyres when they get to around 3mm depth.
Tyre tread depth is important because it allows water to be displaced from beneath the tyre, preventing possible loss of traction. The more tread you have the more water your tyre is able to displace.