Straight-through and cross-over cables are cables that are generally short in length that are used to connect your computer to the network or to another computer.
The straight-through cables are often called Ethernet cables, although I have seen organizations call all cables to hook the PC to the network or another PC Ethernet cables. Since they are short cables and often just from PC to wall you will also hear them called patch cables.
Straight-thru cables are used to connect the PC to the network. This may be by connecting to the switch (box with several outlets for cables to plug in) which allows several computers connected on the same network. The straight-through cable has eight (8) wires in it and they each connect to the same pin in the plugs at the end of the cable. The PC and the switch use different pins to talk and send on so works.
The cross-over cable is used to connect two of the same type boxes together, often PC to PC. If you want to transfer data from one PC to another over a cable you will use a cross-over. Also, if you want to play a game on two computers that are directly connected together you would use a cross-over. This used to be popular with gamers but is not as often now as they use the network.
The cross-over cable switches two pairs of wires on what pins they are connected on both ends. Since it is PC to PC then they both talk on same two pins and both receive on same two pins. A straight thru cable would have them both talking on same pair of wires and that would not work. This way what is send on one end goes to receive wire on the other end.
When you get a networking device and there is a cable included it is normally a straight-though cable. You can tell by looking at the wires at the end of the two plugs and if colors are the same on both ends it is a straight-though cable.
Thank you Robert for the question.