Theoretically, you don't need to have bellows on your enlarger. However, if you don't have them, light will spill out all over the room and potentially destroy any photosensitve materials it falls on. You might have a small problem with contrast or intensity of light that falls on the target (photo paper) due to loss of light but that's a topic for another discussion, all together.
I took the bellows off my enlarger when I was doing the alignment procedure because it allowed better access to the negative stage and the lens board adjustments without trying to reach in and tweak them with a screwdriver. I could just slide the spirit level in and do the adjustment.
But for the above mentioned light leakage, the enlarger operated normally.
When you focus the enlarger, you will move the lens board up and down to bring the focal plane of the lens into alignment with the film plane. When these two planes (or zones) are perfectly aligned, plumb, level and square to each other, your image will be in focus on the baseboard/easel. If the image is not focus, you must turn the focus knob which will rack the lens board up or down until focus is achieved.
The distance between the film plane and the lens focal plane will vary in direct proportion to the focal length of the lens. (i.e. The longer the focal length, the farther apart the lens and the film will be.) The bellows expand or contract to fill the space between the lens and the film plane.
Basically, the bellows are just along for the ride.
As Matt says, if your lens focal length is too long for your bellows to reach, you will either have to get a longer bellows or a shorter focal length lens... Assuming that a lens of the given focal length will correctly project the image from your film without vignetting or distortion.