Today, my classmate and I stained a slide of cheek cells. After we put on a coverslip, our teacher said that we are supposed to remove excess solution using a tissue.
Why should we do this? I am so confused
Well, from personal experience, whenever there was excess solution on the glass slide, our teacher always commented that our slides were messy. So I guess the entire idea is to keep the slide neat, clean and to make it look presentable for observation. Also, in case the excess solution flows out to the entire surface of the glass slide, the stage clips may not be able to hold the slide in place when it is kept on the stage of the microscope (since it would be all slippery). Usually, only such little things go wrong, nothing huge. It is actually more of a basic etiquette or precaution that is followed while preparing a slide, like wiping your mouth after eating. Your observation is not affected in any way.
Neither of the current answers fully answer the question.
The amount of liquid underneath a coverslip should be just sufficient to hold the coverslip and sample onto the slide. If there is too much water, the surface tension would become reduced, allowing the coverslip to fall off the slide.
Additionally, minimising the amount of water between the coverslip and the slide would ensure that the z-axis variation in your sample is minimised, therefore reducing the likelihood that your sample will have different focal points across the sample.
This UCLA guide on microscopy slide mounting explains it (emphasis mine):
Small pieces of filter paper (Whatman #1) are placed around the edge of the coverslip to absorb excess mounting medium. If your specimen is tissue culture cells or frozen tissue sections, this should not harm them. This does two things: a) it allows the coverslip to come as close to the specimen as possible and reduces the depth of the field. You will get less focus aberration if you do this judiciously. b) the coverslip will be a lot less likely to float around on the slide and move which could specimen damage. The surface tension between the coverslip and slide will be much higher. You will also be much better able to seal your coverslip to the slide.
March Ho is right: when viewed at any magnification, that tiny amount of fluid between slide and coverslip is an ocean, where all those things are present that are present... well in an ocean: fluid currents and those critters once just underneath the surface, than again "in the deep". As March put the later: "z-axis variation". Those involved in studying live critters, pond dipping and such (everyone should do it at least a few times!) know the phenomenon all too well.