When installing a custom ROM onto a rooted Android device, they often recommend to upgrade the radio firmware.
What exactly is Android's radio firmware?
The radio firmware controls basic low-level functions like network connectivity, Wi-Fi, and GPS. For several years, though, "radio" means "baseband", and controls network connectivity aspects only, while WiFi and GPS are governed by OS drivers, like any other devices.
Usually upgrading your radio will not give you any new features but will fix connectivity issues, increase range or performance, decrease battery usage, or the like. Some ROM's require you to have the latest radio versions to work.
While a botched radio upgrade can brick your phone, the process is basically the same as upgrading your ROM. Just make sure not to unplug or power down your phone in the middle, make sure you trust the person who released the radio firmware, and try to read some comments or reviews.
As a side note on radio firmwares beware of upgrading them without having seen a test of the version on your network.
Sometimes new radio firmwares add features for some network providers that result in worse bandwidth, disconnections and other disagreement if you use them on another network. Network operators don't provide phones with such broken firmwares (they wait for the next version or just provide the same radio firmware forever) but if you install them yourself it's a risk you take.
But if you want to use the latest firmware all the times before your network operator or phone manufacturer provide the update you may need to take this risk (Video crashed the HTC Desire when used with all but the latest radio rom on froyo...)
If you don't think it is necessary to flash a radio then don't do it. At least I heard that it will not make any difference to your phone storage and speed. But somehow if you have connectivity issues like dropped calls, WiFi connection not searching or GPS does not seem to work then surely you need to flash the radio to another version than you are using at the moment.
If you want to see which radio your phone is working on go to settings > About phone > Baseband version > See the last some digits and then search for your phone Like HTC desire latest radio etc..
Note: I Recommend you should read more about Radio before flashing it. Sometimes there is a chance to brick your phone but don't worry if you have searched enough of it you are not going to lose anything. At least give a weekend or two to search for tutorials on forums like XDA, Android Central, Google, Wiki etc..
Phone service carriers will sometimes update the firmware on your radio. For reasons unknown, improved radio firmware isn't always made available to customers.
The radio firmware will, through software, increase your service coverage, giving you better signal and battery life.