Hi
Once they have been paired, your Apple Watch and iPhone will remain paired until they are manually unpaired. However, they can become disconnected or connected (multiple times) whilst still being paired.
Disconnections can be normal, such as when the watch loses the Bluetooth connection with the paired iPhone and no known W-Fi network is available.
Normal Bluetooth range is around 33 feet / 10 meters. The actual range will vary in practice due to wireless interference (including, for example, due to walls), but you don't necessarily need to have your iPhone on or immediately around you (within arm's reach, for example) for the devices to maintain their Bluetooth connection.
Once they have become disconnected, they should reconnect automatically a short while after being brought close together again.
More information:
About Bluetooth and Wi-Fi on Apple Watch - Apple Support
valem1234 wrote:
.. also, which is the home button and what are the purposes of the buttons?
You may find these resources helpful:
Quick look at Apple Watch (it does not have a Home button):
About your Apple Watch - Apple Support