The new comet C/2020 F3 was first spotted by NASA's NEOWISE satellite in March 2020. It is now visible in the NE sky just before dawn. The C may refer to it's non-periodic nature (so far). What does the F3 mean in its name ? The orbit may be parabolic.
C means "comet": it has a coma which means that volatiles are being released due to solar heating. Other possible letters are "A" for asteroid, "P" for (short) periodic comet, "D" for disappeared comet, "I" for interstellar object and "SN" for supernova.
2020 is the year of discovery
F represent the half-month of discovery, so "A" is the first half of January, and so on. "F" means "the second half of March".
3 means the third comet identified in that half month, and "NEOWISE" is the name of the discoverer, in this case it was discovered by a space telescope that scans the sky looking for Near Earth Objects.
Such designations are considered provisional and can be replaced with a permanent number if the object is found to be in a permanent orbit. So a full designation of Halley's comet is "1P/1682 Q1 (Halley)" as it has permanent number 1, it is periodic, it's orbit was the first published in the second half of August 1682 by Edmund Halley.