The Raspberry Pi can connect to a Wi-Fi network using a USB dongle but using that same dongle you can also turn your Raspberry Pi into a wireless access point. Once set up correctly, this will allow other wireless devices to connect to your Pi and optionally you can route any traffic out through the Ethernet port and on to the internet (via the router from your ISP).
However, before looking at the steps needed to get this working, a word of warning. The configuration needed can be a little complex and if things don’t work as they should then troubleshooting the problem can be difficult. Also for this to work correctly, you need a WiFi USB dongle that can work as an access point. The best place to find information about your particular dongle and the Raspberry Pi is on the embedded Linux Raspberry Pi Wi-Fi adapters page.
To configure a hotspot requires several steps:
Configure the wireless adapter with a static IP address
Install and configure a DHCP server
Install and configure the access point daemon
Configure IP routing between the wireless and Ethernet