A capture card is like a video-in for your computer. A passthrough lets it 'sit' between the console and your TV, without introducing any capture delay on what's shown on your TV (the stuff coming into your PC will have an amount of cap delay regardless of card, though some are extremely low). You CAN use an HDMI splitter instead of a passthrough, if your capture device of choice does not include a passthrough port. That's pretty much what a passthrough port is anyway, just an internal splitter that sends half to the capture device and half to an output port which you then plug into your TV via another HDMI cable.
My own top two units are the Micomsoft SC-512N1-L/DVI, and the Elgato HD60 Pro. Both are internal cards, and both offer passthrough ports (the Elgato has one built-in, and the SC512 on a daughtercard which I have since removed and just use an HDMI splitter to save space in the case). I've also heard good things about the Magewell line, but do not own one (yet), and they're rather pricey.
Do AVOID USB capture devices if at all possible. They tend to have a significant amount of capture delay (around 2 seconds for the more common units) or significant technical glitches (in the case of Avermedia gear). The only general exception to this (if you have a laptop and NEED one) is the XCAPTURE-1.