Traditionally, laptops had screens that did not accept any sort of touch input. Many laptops screens today are still non-touch. The latest Windows operating systems (Windows 8 and Windows 8.1) were designed to work well with touch screens. Many people find using Windows 8/8.1 much more difficult if the computer does not have a touch screen since so much of the navigation is meant to be done with touch input. 


Touch Screens
There are several different types of touch screen technologies. Resistive and capacitive touch screens are the most common types.
Resistive touch screens rely on detecting pressure being applied to the screen. A finger, finger nail, plastic tipped stylus/pen, etc. can all be used with resistive touch screens. Resistive screens cannot recognize lighter touch input and can become damaged because of the pressure needed to use the touch screen.
Capactive screens rely on the conductive properties of objects such as a finger to register the touch. A finger or special stylus (usually rubber tipped, but can be disc or other style) can be used with capactive screens. iPads and iPhones are a good example of this type of touch screen. Most laptop and tablet touch screens today use capactive screens.
Active digitizers can be added to one of the other types of screens (usually capactive). Active digitizers (also know simply as digitizers) only use a special stylus/pen which can be registered when it touches the screen or when it hovers over the screen. Digitizers allow for touch screens to accurately register handwriting (capactive screens alone can be used for handwriting, but there is a significant lag and it is much less precise).
Touch screens also can vary in the number of fingers or input points it can detect at the same time. Most touch screens can either recognize 5 fingers or 10 fingers at a time.
Some touch screens also use palm rejection/detection technology to ignore any input that would be caused by resting the palm of your hand on the touch screen. This is especially useful if you take a lot of notes by hand.



Display Resolution

Laptop/tablet screens can come in different resolutions. The resolution is usually labeled in terms of the height and width of the screen in pixels. The greater the resolution, the sharper the image can appear.

Resolutions usually come in standard aspect ratios. The aspect ratio will tell you whether a screen is widescreen (e.g. 16:9) or not (e.g. 4:3). 

Resolutions may be labeled with just the resolution or they may be labeled with some letters.

HD = High definition. 1280x720 resolution or 1280x800 resolution or 1366x768 resolution (depending on brand).

HD+ = High definition plus. 1600x900 resolution

FHD = Full HD. 1920x1080 resolution. 1080p and 1080i are other names for this resolution.

QHD = Quad HD. 2560x1440 resolution.

FHD++ = Full HD plus plus. 2880x1620 resolution.
UHD = Ultra HD. UHD 4K = 3840x2160 resolution.
Display Brightness
Brightness is measured in nits. The greater the number of nits, the brighter the screen.  
Type of LCD Screen
Most LCD screens today are TN (twisted nematic) or IPS (in-plane switching). Some advantages to the IPS screens are that they do not lighten when touched, may have richer colors, and have a better viewing angle than TN screens. However, IPS screens may use more energy than TN screens and may have some issues with the light coming from behind the screen "bleeding" through. 
LCD screens that are backlit by LEDs are called LED LCDs. LED LCDs typically use less energy, have better brightness, and are considered to have a better color range. LED LCDs can be IPS or TN.