So it seems Apple keep chopping and changing whether they provide the [secret?!] Field Test App....But anyway it is in iOS5.1.1 (and iOS6) and works on iPhone 4S & 4, and probably 3GS (but not tested). You kick it off by typing the magic code (*3001#12345#*) into the Phone dialpad and then hitting Call. Note: It doesn't work if you add it as a contact and try to call it.
When it starts up it presents a pretty basic interface where you can navigate to find out various info about your GSM and UMTS/3G (and presumably CDMA) connections. It also changes the signal strength icon (top left) for a number - the smaller the negative the number the higher the signal (e.g. -44 represents a better/stronger signal than -99). If you tap the number it changes between the bars and the numbers again.
What the heck can you do with it? I guess it is handy sometimes to have numeric signal strength... And check up on some of the other parameters.
One thing you can do is find out the mobile base station your phone is attached to and then potentially match that with an actual cell location. It's a bit long winded.....In the UK the regulator Ofcom has created a fairly useful web page that provides the position of most cell towers overlaid onto a Google map. So to find out which cell you're attached to firstly check if you're on 3G or not (i.e. 3G icon showing or not - you'll need to turn off wifi to see if it is on though it doesn't affect the app):
If you are on 3G then you tap on:
'UMTS Cell environment'->'UMTS RR Info'->'Downlink Frequency'
The number on that line is the frequency in MHz your phone is using to communicate with the UMTS base station.
If you're not on 3G then you tap on:
'GSM Cell environment'->'GSM Cell Info'->'GSM Serving Cell'->'ARFCN'
If your ARFCN is between 1-124 then your phone is on 900MHz band 128-251, then it's using the 800/850MHz band, and if it is between 512-880, then your phone is using the 1800MHz or 1900MHz bands. A few sites give more details like this one on GSM/LTE, or there's GSM list from the gnu radio folks.
Once you've got this far then you can go look up your location in the UK use the the Ofcom sitefinder (or equivalent in your country) and find the cells near you. Then you have click on each on and find your providers ones and then locate the GSM or UMTS cell towers and then match up the frequencies used by those towers. Blimey that was a bit tedious but you should have got there! If you don't find any cell towers nearby or matching then maybe you've found an undocumented cell tower - report it to OfCom on their pages!
[30oct12: Added iOS6 info, and other minor tweaks]