The sketch is loaded to the ROM of the ESP-01, the Arduino is used for programming only, after that the ESP is an independent server. The ESP is connected to the local network. On request from any internet browser connected to the same network, the ESP server responds with a new temperature reading, otherwise the server is listening for requests.
For uploading the sketch to the ESP-01 you need an Arduino Uno or USB to SERIAL adaptor. The Arduino is hard wired Reset so the mc doesn't take part, only the USB to Serial is used. The Serial Monitor in the Arduino IDE is used for debuging and getting the IP address of the ESP. These websites give good guide for preparing and uploading the sketch.
Before loading the code enter your SSID and password that you use to connect wifi devices to your router.
type in your browser the IP address that you find on the Serial Monitor in the Arduino IDE. Normally the IP is 192.168.1.3