A local reports says the blasts came from Russian troops destroying Ukrainian ammunition depots. However, this report is unofficial and only coming from a French News source:
The BBC is now offering these details on the explosions:
A loud bang was heard about 23:10 local time (21:10 GMT), following by a smaller blast, BBC reporters in Simferopol say.
A city resident blogged about hearing an explosion come from the direction of Elevatornaya Street, where an electronic combat military unit is based.
Update, 5:41pm EST:
A writer for Buzzfeed states that he has reports that the explosions were grenades: