The Clipper Card (which was called TransLink up until about a week before its official debut) is a new cashless way to pay your fare on most Bay Area transit agencies. Think of it as FasTrak for public transit.
This should make life a little simpler for anyone making trips involving more than one transit system. I would certainly recommend picking up a Clipper Card if you ever transfer between CalTrain and BART at Millbrae, for example--you may actually make some close connections that you would otherwise miss while fumbling for change and buying another ticket.
<rant>IMHO this is a fairly small benefit for 10+ years development and $150 million (actual transit systems have been built for less $150 million, albeit not around here). With actual leadership we could have instituted a region-wide fare zone system and actually made riding transit more convenient. What we got is basically a high-tech duct-tape solution to a broken system.</rant>
Anyway, here's what you get in the free Clipper Card package:
There's a card with a code on it. You also get a sleeve to store it in, and a box of mints--the implication being, I guess, that if you're on a crowded train, your fellow passengers may appreciate you eating one!
The physical card was free but I presume I need to load some $$$ on it to use it. You can do that at various ticket machines, various stores, or online. Here's a map. If you do it online, you can set it up to automatically reload, like FasTrak. If you want to do it in person, there are only a few select locations that have add-value machines. I think you're really really supposed to do it online.
If you live in the Peninsula or Silicon Valley, note that SamTrans and VTA do not support Clipper (probably because they didn't want to spend millions of dollars on new ticket machines). It could be useful if you make irregular or random trips on CalTrain. Here's the instructions. If you are a regular rider, it strikes me as a little awkward, especially if want to use Clipper as a paperless monthly pass. My employer provides Go passes (thanks, Microsoft!) so it's moot for me.
If you want to pick up a Clipper Card generally, you can apply for one online or get one at local Wallgreens, who appear to be the main "real world" distributors.
One final note: one definite advantage of the Clipper Card is that if you get the "youth version", kids can use it and will automatically be charged only the youth fare. This is particularly useful for BART, which theoretically has discount youth fares, but does not sell youth tickets in stations (because a ticket machine has no idea if you're a kid or not; I have always ended up paying full fare for my daughter on BART).