What I have experienced during teacher trainings is that they say that if we give children a peppermint prior to a test, the spice of the mint and the fumes that the peppermint causes apparently awake the taste buds and alert the brain to the point that they "think" and "remember" better. I also see how in places where people are meant to be in a peaceful state of mind (the spa, and even other type of stores) there is a background scent of mint to entice the potential customer to feel at ease there. As far as if there are medicinal properties in these two plants, I would assume there may be some. However, the accepted notion is that the plant of ginkgo and some properties of garlic are good for memory.
There does seem to be some research that indicates that the scent of peppermint in particular does help the brain to work better, however the tests are not necessarily conclusive, and as #6 has pointed out, regulations forbidding students from eating peppermints were quickly removed. It does seem that there are foods and scents that help our brains work better, but lots of research is yet to be done before we can establish the conditions that would maximise our brain power.
I concur with the posts above. Once in a while a woman will walk by me in a mall or public place wearing my grandmother's perfume. I am instantly transported back to an 8th grade summer I spent in her New Mexico home and all the accompanying memories whenever that happens. Mint, especially peppermint, stimulates overall brain function, not just memory, and so students tend to perform better on exams when they have peppermint because the brain as a whole is functioning more efficiently. Some say that the herb Ginkgo Biloba also helps with memory, though this has not been conclusively proven.
Any smell is a strong memory trigger. For me, the smell of British Sterling cologne brings me instantly back to when I was 10 years old standing next to dad in my childhood home.
For academics, smell can be very effective in memory recall when it comes to testing. I have seen studies where teachers have introduced a smell (like vanilla) into the classroom when students are studying for an upcoming test, and reintroduced the smell during the testing time, and the students recalled in more detail and with more accuracy what they had learned during the initial studying period.
As for peppermint and vanilla in particular, it seems peppermint is a soothiing fragrance and vanilla promotes comfort.
According to research, the scents of vanilla and peppermint help to stimulate the memory. The inhaled scent of vanilla supposedly helps to reduce the stress hormone cortisol; consumption of the vanilla bean is believed to help prevent memory loss. According to aromatherapists, the odor of peppermint can promote attentiveness; like vanilla, consumption of peppermint is also believed to help improve mental clarity.