What does 这一 mean in 在追求这一目标的过程中?
The '一' here is for emphasis


在追求这目标的过程中 = In the process of pursuing this goal 
在追求这(一)目标的过程中 = In the process of pursuing this (one/ single) goal 


The two sentence basically have the same meaning, but the "一" in the second sentence emphasizes the singularity of the object 目标. Affirm it is the 'one' goal stated earlier and stress its importance. 

More example:

此理想 = this goal

此一理想 = this one goal (affirm it is the 'one' goal stated earlier and stress its importance.  )

此人 = this person

此一人 =  this one person (stress the importance of this person in the context, for example, "this one person holds all the keys to your future success")