SLI and CrossFire Support Definition

When a video card has SLI or CrossFire support, more than one video card can be used in the same computer. Using multiple Nvidia video cards is referred to as SLI or "Scalable Link Interface". Using multiple AMD video cards is referred to as "CrossFire". This can greatly increase performance if the program being used supports SLI or CrossFire. Otherwise performance may even become worse.

This is convenient because a computer can be built with one video card at first and still have room to upgrade without getting rid of your old card. Using two of Nvidia's card usually requires the cards to be the same model with a few exceptions. AMD, on the other hand, allows a little more flexibility as long as the first two numbers in the card's name are the same. This means that a Radeon HD 7870 can be paired up with a 7850 but not a 7750. This chart at Tom's hardware explains more about what cards can be paired together.

Check beforehand whether your motherboard supports SLI or CrossFire. Your power supply may also need to support SLI or CrossFire when pairing some of the higher end cards.

Socket Type Definition

A CPU socket is the location where a CPU is secured on the motherboard. A socket is what allows the processor to communicate with the rest of the computer. Sockets make it very easy to install and remove CPU's. Each CPU generation will require a specific socket type. The motherboard and the processor must use the same socket.

Intel's Socket Types:
LGA 1150 - Used by Haswell CPUs (4th Generation i3, i5 and i7's)
LGA 1155 - Used by Sandy Bridge (2nd Generation i3, i5 and i7's) and Ivy Bridge CPUs (3rd Generation i3, i5 and i7's)
LGA 2011 - Used by high end i7's

AMD's Socket Types:
AM3+ Used by Vishera, Zambezi and other CPU's
FM1 Used by Llano CPU's
FM2 Used by Trinity and Richland CPU's

Architecture or Core Definition

The architecture or core is how the ISA or instruction set architecture is designed in the CPU. Newer architectures greatly help with efficiency and allow for more performance per gigahert. It is important to always buy the latest architecture. Here is a wiki article containing a list of Intel and AMD's architectures.