Think of the one-touch taps as events, similar to how IFTTT has long worked, which caused some action based on a event. You might have a notification appear on your handset, for example, when your favorite sports team scored points. The trigger event in that case would be the scoring activity and the result would be the automatic notification.
The DO Button tap is now a trigger event that makes something happen, depending on how you've configured it with an IFTTT recipe.
Here a some examples from the IFTTT team:
Turn on your lights with just a tap+
Get yourself out of awkward situations with a phonecall
Set your Nest Thermostat to the perfect temperature
Email your roommates when you're at the local grocery
Block off the next hour as busy in Google Calendar
Track your work hours in a Google Drive spreadsheet
Get a text with the location of where you parked the car
Ask colleagues on Slack if they want coffee
Toggle on or off most internet enabled devices
Tweet a map of your current location
Turn off your oven with a push of a button
A press of the DO Button kicks off any event that the platform supports through its various channels. It's an easy way to automate actions that up to now required some other trigger event.
Since IFTTT is cloud-based -- that's where the rules and events are all stored -- it only works with connected devices. Given that an Android Wear watch is generally paired with a phone, and that many Android Wear devices also support Wi-Fi connections, that limitation shouldn't be an issue.