UDID is the short form for Unique Device Identifier. It is a 40-character long value containing alpha-numeric symbols (a-z and 0-9). The UDID is being used by developers to register devices for testing their Apps. Only on registered devices developers can run Apps that are not in Apple's AppStore yet. Developers currently have up to 100 UDIDs they can register.
Note, that UDID of your device may change in the case of changing some part of it, for example after repair, because on some models UDID is generated partically from MAC-addresses of network interfaces your device have.
iPhone or iPad Serial Number identifies device model. It is provided by manufacturer. As serial number of any device it may contain party number or any other info related to device model you're hold in your hands. Some Apple™ support resources are asking Serial no. of your device to give you more relevant info or provide you more accurate support.
IMEI is The International Mobile Station Equipment Identity
Avoid spreading of IMEI and UDID to third-parties you don't trust, because you may facilitate the work of thefts and fraudsters. Anyway, if bad things happen contact Apple support and police and be guided by the laws of the country where incident provoked.
You may refer to the official Apple™ documentation to get more info on how to obtain UDID, IMEI and other device specific IDs.