1. Profile 1.0 - This profile covers all Blu-ray Disc players made before November 2007. Players in this category have one video decoder and no internet connection. This means that these players cannot access PIP (Picture-in-Picture) imbedded content on Blu-ray Discs, nor can they access Web-enabled content included on some Blu-ray Discs. As a side note, all HD-DVD players are required to have these capabilities built-in from day one.
2. Profile 1.1 - This profile adds a second audio/video processor and 256 MB of memory storage to all Blu-ray Disc player models introduced after November 1st, 2007. This allows access of imbedded PIP commentary content and other interactive features included on some Blu-ray Discs (also referred to as "Bonus View"). In addition, some profile 1.1 players allow direct access to web-available firmware upgrades. However, it is not required that a Blu-ray Disc player have an internet connection to qualify as a Profile 1.1 compatible player.
3. Profile 2.0 - This profile is referred to as "BD Live". Essentially it is similar to Profile 1.1, but adds a 1GB memory storage capacity and also requires the inclusion of an Ethernet connection, which enables more flexibility in accessing additional features that may be included on Blu-ray Discs and more sophisticated web-enabled feature access via the high-speed internet port. This brings the Blu-ray Disc format to the same place as HD-DVD players have been from the initial introduction of that now-defunct format.
The intention is that all Blu-ray Discs, no matter what Profile they are tied to, will be playable on all Blu-ray Disc players. However, any special disc content requiring Profile 1.1 or 2.0 will not be accessible on Profile 1.0 players, and Profile 2.0 specific content will not be accessible by either a Profile 1.0 or 1.1 equipped player.
On the other hand, some Profile 1.1 players may be firmware and memory upgradeable (via external flash card), provided they already have an ethernet connection and USB input connection, while the Sony Playstation 3 Blu-ray equipped game console can be upgraded to Profile 2.0 with just a downloadable firmware upgrade.
4. Profile 3.0 (BD-Audio) - In addition to the above profiles, Profile 3.0 has been developed strictly for audio-only Blu-ray Disc application. What this profile allows is the manufacture of Blu-ray Disc players for the purposes of audio-only playback and is really targeted for the niche-audiophile market. In other words, a Profile 3.0 compatible Blu-ray Disc player may not be compliant with the 1.0, 1.1, or 2.0 Profile video requirements listed above. So far, this profile has only been implemented in testing environments.
NOTE: The HD-DVD format was not designed with a profile system. All HD-DVD players that were released since their introduction, until their discontinuation, from the least expensive, to the most expensive, allowed users to access all interactive and internet features associated with HD-DVDs that incorporated such features.
For a more on the technical aspects of both Blu-ray and HD-DVD, check out How Blu-ray Works and How HD-DVD Works as posted by How Stuff Works, and Blu-ray and HD-DVD Audio Explained - High Def Digest.