There are several things that could cause the fret buzz (vibrating sound from the strings slightly touching a fret).
The nut may be worn or improper. This only effects an open string. If there is buzz with the string depressed at any fret, the nut is not the problem. To check the nut, depress the string at the 2nd fret. You should be able to see just the tiniest sliver of light between the string and the 1st fret. If you do, that slot in the nut is all right. Installing a nut is harder than you may think. It needs to be shaped and the slots cut to the appropriate depth and the the appropriate width for the size strings you play. A nut replacement should be done by a guitar tech.
The neck relief may be incorrect. The neck may not have enough curvature to raise the strings above the frets from 1 to 12. The relief is set by adjusting the truss rod. I do not recommend you tackle that. Tinkering with the truss rod if you do not know what you are doing is a fast way to trash the neck.
A fret could be damaged. A ding or dent in a fret will allow the string to sit too low and cause the string to rub against subsequent frets. Or a fret could be high. A high fret will rub against the strings when you depress the string at a fret closer to the nut. Fret work should be done by a qualified guitar tech.
Neck may be twisted, warped or have a back bow. This is pretty much a kiss of death to an inexpensive neck. The repair cost exceeds the cost of a replacement neck.
Action may be too low. The action is the string height above the frets from the 12th fret to the end of the neck (20th, 21st, 22nd or 24th fret). The action is set by adjusting the string height at the saddle. But this will not cure problems from the 1st fret down to the 12th fret.
The odds are your guitar needs a good set up. Take it to a shop and let their guitar tech do a set up on it.