The "short-term effect" of something is the immediate result of something. For example, a short-term effect of drinking alcohol would be the slurring of speech, because that happens soon after you get drunk.
The "long-term" effect of something is the gradual consequence of something. For example, again using alcohol, if you drank large quantities of alcohol consistently for 10 years, the long-term effect would be liver damage, because alcohol can harm the liver in large quantities.
I hope this helps!