Maximum Image Resolution
Image resolution refers to the amount of pixels that make up an photo taken on a digital camera. It is measured as the width x the height of the image - so a 1280 x 720 resolution camera can take a photo that is 1280 pixels wide and 720 pixels tall.
Image resolution is a measurement of how detailed the photos taken by the camera are. A higher resolution means a single image is comprised of more pixels, leading to greater detail. This is important with portrait cameras, since it allows every nuance and subtlety of the subject, lighting and position to be brought to the fore by the camera, rather than being lost in a low-quality image.
Minimum Aperture Number
In photography, the aperture number refers to the size of the hole in the front of the camera lens, through which light is let through. The larger the aperture, the more light can pass through into the camera's sensor. Photographers can modify this aperture to control the 'depth of field' for their shot - this is how much of the shot is held in focus, and how much is blurred.
Aperture numbers are measured in f/stops: rather confusingly a smaller aperture number translates to a larger hole, therefore a larger amount of light will be let through.
A small minimum aperture number means the lens has a bigger aperture which lets more light into the lens. This will allow a faster photograph to be taken which will allow portraits with blurred backgrounds.
The pre-flash is a small, short flash triggered by the camera a fraction before the main flash when the photo is taken.
Pre-flash is a small burst of light before the main flash - it causes the subject's pupils to contract, meaning there is less chance of red-eye from the portrait. Very helpful with a portrait camera, since eyes will be a central focus in many of your photos.
'Smile detection' is a special mode for a digital camera that can detect when the subject is smiling, and take the photo automatically when it detects a smile.
Smile detection automatically detects and takes a photo when it registers a smile. A helpful utility in a portrait camera, since it gives you a way to capture your subject as they smile, rather than missing the moment due to poor timing or bad reflexes.
Handheld Remote Control
'Handheld Remote Control' denotes whether the camera comes with a device to control the camera remotely.
A handheld remote can be useful when taking selfies or group shots, since you don't have to be holding the camera to take the shot. It is helpful for self-portaits, and also for triggering a shot without having to physically touch the camera, reducing the chance of accidental blurring due to movement.
A self-timer is a system to allow a digital camera to count-down before it takes a photo.
A self-timer can be useful when taking selfies or group shots, since you don't have to be holding the camera to take the shot. Helpful for self-portraits, and including yourself in group portrait shots.