Lumens will be a measure of the light output of the projector. The larger the image you're making, as well as the amount of ambient light will factor into the lumen output you'll need. For a home theater with relatively low ambient light (normal home lighting) a 2,000 lumen projector will work well. The recommended image size for this would be between 90-120" (remember, though, that the larger the image the more spread out the light will be. So if this is going in a room with bright lights, an image size in the 90's may be best)
For a projector going in a large venue where a large (150-200") image will be created, a light output of about 4,000 lumens will be your best bet.
Resolution is a measure of the number of pixels the projector can create. Basically, the higher the number, the greater clarity you'll see. The vast majority of home theater projectors will by 1080p, also known as 1920x1080. This means that you will have 1920 pixels horizontally, and 1080 pixels vertically (this is what gives us the signature 16:9 HD aspect ratio).
For applications such as schools and office, a high resolution may not be necessary, and in that case you can look for XGA (1024x768) and WXGA (1280x800) projectors.
Another important specification is the aspect ratio of the projector. If you're going to be using a projector in a home theater, it would be best to get a projector that has a native 16:9 aspect ratio. This is the same ratio found on HD TVs:
The other two most common (usually seen in office/education settings) are:
You'll typically see this as the type of widescreen used outside of home theater settings (office/school)
Keystone is an adjustment you can make on the projector if it is necessary to mount it at an angle:
Although this is an included feature, it does degrade image quality if a lot is being used. For the best picture, it will be best to do your due diligence and setup everything so none is needed.