The verb apurar or apurarse (reflexive form) and darse prisa mean "to hurry". When used in the following context, they mean exactly the same:

apurarse
subject + reflexive pronoun + verb "apurar" indicative form

darse prisa
subject + reflexive pronoun + verb "dar" indicative form + "prisa"

Yo me apuro con los mandados.
I hurry with the errands.

Yo me doy prisa con los mandados.
I hurry with the errands.

The reflexive pronoun can also be used after the verb.
Let's see a few examples:

Tengo que apurarme.
I have to hurry.

Tengo que darme prisa.
I have to hurry.

Juan, tienes que apurarte.
Juan, you have to hurry.

Juan, date prisa.
Juan, hurry!