A Wi-Fi hotspot allows you to connect computers or tablets to the Internet using Wi-Fi thru your phones 3G or 4G connection.

You normally have to pay for a data plan that includes the HotSpot feature. Then configure your iPhone 5 or above to turn it on.
See How to set up your iPhone as a Wi-Fi mobile hotspot (iOS 8 tutorial)

Tethering is a similar process using a USB connection instead of a Wi-Fi connection.

There are some 3rd party WiFi hotspot apps or other solutions which allow you to do it on your own. Some mobile phone companies will charge you an extra fee $20-30 if they detect you doing this.

3rd Party Solutions for iPhone:
Requires jailbreak

 TetherMe - Required jailbreak
  Covers tracks so don't get a $20 charge
 MyWi doesn't cover tracks
 
No jailbreak
Edit preferences.plist
run  iBackupBot app to backup to your mac or windows machine
edit preferences.plist there
locate APN
delete ...

APN - Access Point Name - The name of a gateway between a GPRS, 3G or 4G mobile network
and another computer network, frequently the public Internet.
Esamples
Verizon - vzwinternet
AT&T - pdpwap1
T-Mobile - epc.tmobile.com

Read more at: http://www.4gtricks.com/2012/12/verizon-4g-apn-settings-for-iphone.html
see Enable Personal Hotspot (Wi-Fi Tethering) On iPhone For Free [No Jailbreak Required] | Redmond Pie
Links:


last updated 24 Sept 2014