How I'd describe tri-state ...
An output pin can be set high (+V) and it will source (deliver) current, such as when illuminating a LED to 0V. Anything connected to the output will be pulled up towards +V.
An output can be set low (0V) and it will sink current, such as that which flows through a LED connected to +V which will cause it to illuminate. Anything connected to the output will be pulled down towards 0V.
An output can also be 'tri-stated', also known as 'high impedence', 'Hi-Z' or just 'Z'. In this state, the output neither sources nor sinks current. Anything connected to it will 'float' as if it wasn't even connected.
Okay, that's a pefect world and there will be uA's of current flow and a tendancy to pull whatever is connected to +V/2, but it's so small we can ignore it in most cases.
The way the PICAXE/PICmicro works is that it has two internal control lines to affect the output; one will turn on the circuitry which forces it high and sources current, the other will turn on the circuitry which pulls it low and sinks current. If neither control lines are activated the output is neither sourcing nor sinking current and is thus tri-stated.
It just so happens that when a PICAXE 'INPUT' command is used it turns off both control lines, as opposed to the 'HIGH' and 'LOW' which turn one of them on.
Also, because a tri-stated output allows whatever is connected to it to float, whatever that level is can be read back in, using the 'pins' variable.