The women were afraid as a result of their encounter(s) inside the tomb.
At the core of Mark's account is the young man inside the tomb. From strictly human experience it is understandable the women encountering a young man, likely supernatural, inside the tomb would be cause for alarm, fear, or terror.
Mark and Luke both record encounters the women had inside the tomb. Each also states the women were afraid:
And entering the tomb, they saw a young man sitting on the right side, dressed in a white robe, and they were alarmed (ἐξεθαμβήθησαν). And he said to them, “Do not be alarmed (ἐκθαμβεῖσθε). You seek Jesus of Nazareth, who was crucified. He has risen; he is not here. See the place where they laid him... And they went out and fled from the tomb, for trembling (εἶχεν) and astonishment (ἔκστασις) had seized them, and they said nothing to anyone, for they were afraid (ἐφοβοῦντο). (Mark 16:5-6, 8 ESV)
And as they were frightened (ἐμφόβων) and bowed their faces to the ground, the men said to them, “Why do you seek the living among the dead? He is not here, but has risen. Remember how he told you, while he was still in Galilee, that the Son of Man must be delivered into the hands of sinful men and be crucified and on the third day rise.” (Luke 24:5-7 ESV)
Mark's states "they were afraid" using the word ἐφοβοῦντο [G5399-phobeo] where Luke states the women were "frightened" using the word ἐμφόβων [G1719-emphobos]. Mark's statement seems to say they left in fear while Luke is clear they were afraid inside the tomb. If this is correct, then the use of different words ἐφοβοῦντο and ἐμφόβων follows how each account records the women's fear. Inside the tomb the women were ἐμφόβων (Luke) and they fled in ἐφοβοῦντο (Mark).
Mark provides additional details saying they fled with "trembling and astonishment" using the words εἶχεν [G2192-echo] and ἔκστασις [G1611-ekstasis] These reactions are consistent with fear.
In a similar fashion when describing the women's fear, Luke gives the additional detail: "they bowed their faces to the ground." This too is consistent with being afraid.
Finally, Mark states the women were "alarmed" ἐξεθαμβήθησαν while inside the tomb. That reaction is recognized by the man who tells them "do not be alarmed." This word can mean to terrify or be struck with terror.
[G1568-ekthambeo] It is used once in the LXX where the Hebrew is usually translated as fear or terrify:
Behold, no fear of me need terrify you... (Job 33:7 ESV)
οὐχ ὁ φόβος μού σε στροβήσει
Inside the tomb the women encountered one man or two men. Or since Luke states they bowed their faces to the ground, Mark and Luke may be describing two different encounters separated by bowing their faces to the ground. In this case, there would be even greater reason for them to be afraid.
Therefore we can say they women were afraid of the man/men who spoke to them inside the tomb and a combined account of Mark and Luke's description could flow like this:
...entering the tomb they were frightened (ἐμφόβων) and bowed their faces to the ground...they saw a young man sitting on the right side, dressed in a white robe, and they were alarmed (ἐξεθαμβήθησαν)...they went out and fled from the tomb, for trembling (εἶχεν) and astonishment (ἔκστασις) had seized them, and they said nothing to anyone [the man/men inside the tomb], for they were afraid (ἐφοβοῦντο).