To be stiff-necked is to be obstinate and difficult to lead. The Bible often uses this figure of speech when describing the attitude of  people.

What does a stiff-necked person mean?

haughty, stubborn

Definition of stiff-necked

Where did the saying stiff-necked come from?

stiff-necked (adj.)

"stubborn, obstinate,"

It is not only in Exodus 32 that God calls the Israelites "stiff necked people." The expression can be found in 18 places in the Bible: Exodus 32:9

Exodus 33:3

Exodus 33:5

Exodus 34:9

Deuteronomy 9:6

Deuteronomy 9:13

Deuteronomy 10:16

Deuteronomy 31:27

2 Kings 17:14

2 Chronicles 30:8

2 Chronicles 36:13

Nehemiah 9:17

Nehemiah 9:29

Psalms 78:8

Proverbs 29:1

Jeremiah 7:26

Jeremiah 19:15

Acts 7:51

God's statement in Isaiah 48:4 seems to bring out the meaning and derivative of the expression "stiff necked people:"

Because I know that you are obstinate, and your neck is an iron sinew and your forehead brass, (see Isa 48:4 Cross References (24 Verses)

Here good definitions of the expression:

International Standard Bible Encyclopedia

STIFF-NECKED

stif'-nekt (qesheh `oreph, literally, "hard of neck"): As it is figuratively used, both in the Old Testament and in the New Testament, the word means "stubborn," "untractable," "not to be led." The derivation of the idea was entirely familiar to the Jews, with whom the ox was the most useful and common of domestic animals. It was especially used for such agricultural purposes as harrowing and plowing (Judges 14:18

 1 Corinthians 9:9

The plow was usually drawn by two oxen. As the plowman required but one hand to guide the plow, he carried in the other an "oxgoad." This was a light pole, shod with an iron spike. With this he would prick the oxen upon the hind legs to increase their speed, and upon the neck to turn, or to keep a straight course when deviating. If an ox was hard to control or stubborn, it was "hard of neck," or stiffnecked. Hence, the figure was used in the Scriptures to express the stubborn, untractable spirit of a people not responsive to the guiding of their God (Exodus 32:9

 Observes:

However, most of the commentators throughout the ages understand “stiffnecked” to refer not to the body of the Jewish People, but to its character. Most teach that it was not a condition imposed upon us from the outside, but a circumstance of our own choosing. Where the commentators differ, however, is in their opinions as to whether being stiffnecked is an ugly trait to be reviled or a sign of strength to be admired.