Like a man, a woman can also have an erection of the clitoris and the nipples.
The clitoris of a female is homologous to the penis as both contain the same tissues. The clitoris has a head and a body, which is surrounded by erectile tissues and just like the penis, has erectile tissues (corpus spongiosum and corpus cavernosa) which fill with blood to become erect during sexual stimulation.
It further becomes harder, larger, redder and more sensitive.
The nipples do not have tissues in them that fill with blood. Instead, sexual stimulation causes the nervous system to contract muscles in the nipples to make them firm. Thus, one will observe erect, hard nipples on a woman during arousal. Additionally, the labia becomes engorged and there is vaginal lubrication.
In some women there will be nervousness, increased heart rate, pupil dilation, a full-body blush etc during arousal.
So, of course women do get erections, but will certainly not develop a bulge like men; and now you know how.