The 3 main laundry appliances (washing machine, tumble dryer and washer dryer) all share a fair amount of terminology among each other. A few of the below will be specific to one type of machine, but whenever that is the case it has been clearly stated. Everything else can be applied to all typed of laundry machines.
Maximum Load Capacity
This number is relevant to the maximum amount of laundry that can be put through the machine in one wash or dry cycle. The capacity of a washing machine tends to very between 5kg-11kg, the amount you decide you need can roughly be broken down to family size.
5 or 6kg is good for 2 people or an average 25-30 T-shirts.
7kg is good for a 3 person family or the equivalent of 35 T-shirts.
8 or 9kg is suitable for a 4-5 person family being able to wash between 40-45 T-shirts.
10kg+ machines are suitable for households of 5 or more people which allows you to wash an average of 50-55 T-shirts.
The above figures are just a rough guideline which can be used to judge what size you would need.
If your looking at a washer dryer they normally have 2 separate load capacities, a wash and a dry. Due to the way the machines work they tend to have a lower dry capacity than wash capacity, so if your looking to get a washer dryer where you can put 6kg washing in and have it wash and dry, then you may need to buy a machine with a larger wash capacity that can sustain the dry amount you require.
Spin Speed / Revolutions Per Minute
The spin speed is the way a machine measures how fast the drum spins mid cycle on a washing machine. It's measured by the amount of revolutions per minute (RPM) it performs. You will find it listed on washing machines and washer dryers, but it is only relevant to the washing cycle. You can generally find them listed with a RPM between 1000 and 1600.
A fairly self explanatory feature, but some machines will be listed as having a display. This means the machine will have a digital display on the front panel which will show various information relating to the wash programme, most notable and useful being the remaining time.
Another feature that's fairly self explanatory, but a start delay feature allows you to set the load up to be wash/dried but then tells the machine to delay the cycle for a set amount of hours. Perfect for if you want to set up a cycle to run during the night after you go to bed when electricity is cheaper or possibly so the cycle starts when your out and finishes at the same time you are due to return.
Energy Efficiency Class
The energy efficiency class is a rating between A+++ and G that's given to a machine based on it's energy performance. A+++ being the highest rating and G being the worst. Every washing machine or tumble dryer will be given an energy rating on the scale above to let you know how energy efficient it is.
Another factor that will be taken in to account when the energy rating is being decided is the water consumption. This is a statistic relevant to washing machines (so will be shown for washing machines and washer dryers) which tells you how much water is consumed on average by the machine. This will be shows as either a per cycle rate, a per year rate or both.
Automatic Dosage System
An automatic dosage system (sometimes goes under slightly different names that the manufacturer has coined) is a system in a washing machine that detects and analyses your wash load and automatically applies the correct amount of detergent for the load. Not only does this make your life easier, but as it always calculates and applies the correct amount you know you will never be wasting your detergent by applying too much.
Heat Pump Dryer
A feature specific to tumble dryers, a full breakdown and explanation of heat pump dryers can be found here.